The total volume of the dill spears is 425 cm³.
To find the total volume of the dill spears, we can subtract the volume of the pickle juice from the volume of the jar.
The jar is in the shape of a cylinder with a base area of 45 cm² and a height of 13 cm. Therefore, the volume of the jar can be calculated using the formula:
Volume of the jar = base area * height
Volume of the jar = 45 cm² * 13 cm
Volume of the jar = 585 cm³
Now, we know that the measuring cup collected 160 cm³ of pickle juice. So, we subtract this volume from the total volume of the jar to find the volume of the dill spears.
Volume of the dill spears = Volume of the jar - Volume of the pickle juice
Volume of the dill spears = 585 cm³ - 160 cm³
Volume of the dill spears = 425 cm³
Therefore, the total volume of the dill spears is 425 cm³.
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A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-course meal?
There are
ways a person can order a two-course meal.
There are 70 ways a person can order a two-course meal from the given restaurant.
To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.
First, we need to select one appetizer from the 10 available options.
This can be done in 10 different ways.
Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.
Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.
Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.
So, there are 70 ways a person can order a two-course meal from the given restaurant.
It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.
If there are any restrictions or limitations on the choices, the number of combinations may vary.
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A hyperbola is defined by the equation ... 100 pts
Answer:
See attachment for the graph of the hyperbola.
Step-by-step explanation:
Given equation:
[tex](x-7)^2-\dfrac{(y-4)^2}{9}=1[/tex]
As the x²-term of the given equation is positive, the transverse axis is horizontal, and so the hyperbola is horizontal (opening left and right). Note, if the y²-term was positive, the hyperbola would have been vertical.
The general formula for a horizontal hyperbola (opening left and right) is:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a horizontal hyperbola}\\\\$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h\pm a, k)$ are the vertices.\\\phantom{ww}$\bullet$ $(h\pm c, k)$ are the foci where $c^2=a^2+b^2.$\\\phantom{ww}$\bullet$ $y=\pm \dfrac{b}{a}(x-h)+k$ are the asymptotes.\\\end{minipage}}[/tex]
Comparing the given equation with the standard equation:
h = 7k = 4a² = 1 ⇒ a = 1b² = 9 ⇒ b = 3To find the value of c, use c² = a² + b²:
[tex]\begin{aligned}c^2&=a^2+b^2\\c^2&=1+9\\c^2&=10\\c&=\sqrt{10}\end{aligned}[/tex]
The center is (h, k). Therefore, the center is (7, 4).
The formula for the loci is (h±c, k). Therefore:
[tex]\begin{aligned}\textsf{Loci}&=(h \pm c, k)\\&=(7 \pm \sqrt{10}, 4)\\&=(7- \sqrt{10}, 4)\;\;\textsf{and}\;\;(7 +\sqrt{10}, 4)\end{aligned}[/tex]
The formula for the vertices is (h±a, k). Therefore:
[tex]\begin{aligned}\textsf{Vertices}&=(h \pm a, k)\\&=(7 \pm 1, 4)\\&=(6, 4)\;\;\textsf{and}\;\;(8, 4)\end{aligned}[/tex]
The asymptotes are:
[tex]\begin{aligned}y&=\pm \dfrac{b}{a}(x-h)+k\\\\y&=\pm \dfrac{3}{1}(x-7)+4\\\\y&=\pm 3(x-7)+4\\\\\implies y&=3x-17\\\implies y&=-3x+25\end{aligned}[/tex]
Therefore:
[tex]\textsf{Center} = (7, 4)[/tex][tex]\textsf{Vertices} = (6, 4) \;\textsf{and}\;(8, 4)[/tex][tex]\textsf{Foci} = (7\pm \sqrt{10}, 4)[/tex][tex]\textsf{Asymptotes:}\;\;y =3x-17\;\;\textsf{and}\;\;y= -3x +25[/tex][tex]\textsf{Transverse axis:} \;\; y = 4[/tex][tex]\textsf{Conjugate axis:}\;\; x = 7[/tex]The graph of the hyperbola (x - 7)² - (y - 4)²/9 = 1 is attached below
What is the graph of the hyperbola?The graph of a hyperbola is a curve that consists of two separate branches, each resembling a symmetrical curve. The general equation for a hyperbola in standard form is:
[(x - h)² / a²] - [(y - k)² / b²] = 1
The center of the hyperbola is represented by the coordinates (h, k). The parameters a and b determine the size and shape of the hyperbola.
Based on the standard form equation, there are two types of hyperbolas:
1. Horizontal Hyperbola:
When the major axis is parallel to the x-axis, the hyperbola is horizontal. The equation in this case is:
[(x - h)² / a²] - [(y - k)² / b²] = 1
The graph of a horizontal hyperbola opens left and right. The branches are symmetric about the x-axis and the center (h, k) is the midpoint between the branches.
2. Vertical Hyperbola:
When the major axis is parallel to the y-axis, the hyperbola is vertical. The equation in this case is:
[(y - k)² / b²] - [(x - h)² / a²] = 1
The graph of a vertical hyperbola opens up and down. The branches are symmetric about the y-axis and the center (h, k) is the midpoint between the branches.
The graph of the given hyperbola is attached below.
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debbie wants tp compare the simple interest to compound interest on 60,000 investment
Answer:
this question is incomplete
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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please help!!!!!!!!!!!!!!!!!!!!!!
The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.
The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.
The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.
What are systematic, random and cluster samples ?A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.
A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.
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Question 4 a) Show that y₁= 1/t is a known solution of -t²y" + 3ty' + 5y = 0, where t > 0, and find the second solution.
y₁ = 1/t is indeed a known solution of the given differential equation.
The second solution can be found using reduction of order or other methods specific to the equation.
Let's find the first and second derivatives of y₁ with respect to t:
y₁ = 1/t
First derivative:
y'₁ = d/dt (1/t) = -1/t²
Second derivative:
y''₁ = d/dt (-1/t²) = 2/t³
Now, let's substitute y₁, y'₁, and y''₁ into the differential equation:
-t²y'' + 3ty' + 5y = 0
Substituting the values:
-t²(2/t³) + 3t(-1/t²) + 5(1/t) = 0
Simplifying the expression:
-2/t + (-3/t) + 5/t = 0
(-2 - 3 + 5)/t = 0
0/t = 0
We can see that the expression simplifies to 0/t, which is equal to 0.
Therefore, y₁ = 1/t is indeed a known solution of the given differential equation.
To find the second solution, we can use the method of reduction of order. Let's assume the second solution is of the form y₂ = v(t)y₁, where v(t) is a function to be determined.
Substituting this into the differential equation, we have:
-t²(y₂'' + v'y₁' + v''y₁) + 3t(y₂' + vy₁') + 5y₂ = 0
Expanding and rearranging the terms, we get:
-t²(v''y₁ + v'y₁' + v'y₁ + vy₁'') + 3t(vy₁' - v'y₁) + 5vy₁ = 0
Simplifying further:
(-t²v''y₁ - 2t²v'y₁' + 3tvy₁' + 5vy₁) + (-t²v'y₁ + 3tvy₁ - 5v'y₁) = 0
Combining like terms:
-t²v''y₁ - 2t²v'y₁' - t²v'y₁ - t²v'y₁ + 3tvy₁' + 3tvy₁ + 5vy₁ - 5v'y₁ = 0
Simplifying:
-t²v''y₁ - 3t²v'y₁' + 6tvy₁' + (5v - 5v')y₁ = 0
Since y₁ = 1/t, we have:
-t²v''(1/t) - 3t²v'(1/t²) + 6tv(1/t²) + (5v - 5v')(1/t) = 0
Simplifying further:
-v'' - 3v' + 6v(1/t) + (5v - 5v')(1/t) = 0
Reducing the equation:
-v'' - 3v' + 6v/t + (5v/t - 5v'/t) = 0
-v'' - 3v' + (6v + 5v - 5v')/t = 0
-v'' - 3v' + (11v - 5v')/t = 0
To simplify the equation, we can multiply through by t:
-tv'' - 3tv' + 11v - 5v' = 0
Now, we have a differential equation in terms of v(t) only. To solve this equation, we can apply appropriate techniques such as separation of variables, integrating factors, or other methods depending on the specific form of the equation. Solving for v(t) will give us the second solution to the original differential equation -t²y" + 3ty' + 5y = 0.
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Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
Submit Question
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
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Amy bought a new car for $21,000
. She paid a 10%
down payment and financed the remaining balance for 36
months with an APR of 3.5%
. Determine the monthly payment that Amy pays. Round your answer to the nearest cent, if necessary.
Answer:
Step-by-step explanation:
To determine the monthly payment Amy pays, we can use the formula for calculating the monthly payment on a loan. The formula is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate
n = Number of monthly payments
Given information:
Principal amount (loan amount) = $21,000
Down payment = 10% of $21,000 = $2,100
Remaining balance = $21,000 - $2,100 = $18,900
APR = 3.5%
Number of monthly payments (n) = 36
To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year):
Monthly interest rate (r) = APR / (12 * 100)
Substituting the values into the formula:
r = 3.5 / (12 * 100) = 0.0029167 (rounded to 7 decimal places)
M = (18,900 * 0.0029167 * (1 + 0.0029167)^36) / ((1 + 0.0029167)^36 - 1)
Using a calculator to evaluate the expression within the formula:
M ≈ $539.26
Therefore, the monthly payment that Amy pays is approximately $539.26.
You give up a full time salary of $45,000 a year to go to school for 2 years. The total cost of going to school is $30,000. If you want to be able to recover your investment in 5 years or less, what is the minimum salary you would need to earn upon earning your degree?
Answer:
Step-by-step explanation:
To recover your investment in 5 years or less, you would need to earn enough to cover the cost of going to school ($30,000) as well as make up for the lost salary over the 2 years of schooling ($45,000/year * 2 years = $90,000).
Therefore, the minimum salary you would need to earn upon earning your degree is the sum of the cost of going to school and the lost salary:
Minimum salary = $30,000 + $90,000 = $120,000.
In order to recover your investment in 5 years or less, you would need to earn a minimum salary of $120,000 per year.
To recuperate the total cost of $120,000 ($30,000 tuition + $90,000 forgone salary) over 5 years, you would need to earn $24,000 more per year on top of your original $45,000 salary. This implies that the minimum salary you need to earn after graduating is $69,000 per annum.
Explanation:To determine the minimum salary, we first need to calculate your total forfeiture over the 2 years of school, which equates to real costs and opportunity costs. Firstly, the real cost is the tuition of $30,000. Secondly, the opportunity costs are the 2 years of salary you're forgoing, best understood as the wages you would've made if you hadn't gone to school. Assuming the salary of $45,000 per year, the total opportunity cost for the 2 years would be $90,000.
Therefore, the total investment is calculated as the sum costs of tuition and forgone salary i.e. $30,000 (tuition) + $90,000 (forgone salary) = $120,000. So to recover this investment in 5 years, you would need to earn an addition of $120,000 above your original salary. Meaning, you will have to recover $120,000 / 5 years = $24,000 per year on top of your initial salary to recover your total costs in the stated timeframe.
Therefore, the minimum salary you need to earn after earning your degree is equal to your original salary plus recovered investment per year: $45,000 (original salary) + $24,000 (increase) = $69,000. Hence, upon completion of your degree, you will have to earn at least $69,000 per year to recover your total investment within 5 years.
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Chef Phillippe has 65 eggs and 46 lbs of flour in his bakery. He has a
recipe for Chocolate cake that requires 3 eggs and 2 lbs of flour. He has
another recipe for Red Velvet Cake that requires 4 eggs and 3 lbs of
flour. If all the supplies are used up making some ratio of both cakes,
how many Chocolate cake can he make?
Answer:
Step-by-step explanation:
12
The manager of an ice cream shop found that the probability of a new customer ordering vanilla ice cream is 3/22. What are the odds against a new customer ordering vanilla ice cream?
Answer:
Step-by-step explanation:
[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]
Odds are 19 to 3.
The pie charts below show information about the animals that were treated in a veterinary surgery during one weekend. 300 animals were treated on Saturday. 125 animals were treated on Sunday. What percentage of all the animals treated during the weekend were tortoises? Give your answer to the nearest 1%. 22% 19% Saturday 3% 56% Animals treated Sunday 4% 48% 28% 12% 8% Key Tortoise Rabbit Cat Dog Hamster Not drawn accurately
16
Find x.
25
X
X
x = [?]√]
The value of x in the right triangle using pthagorean theorem is 3√41.
What is the value of x?The figure in the image is that of a right triangle with of its interior angle at 90 degrees.
Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the figure:
Hypotenuse c = 25
Leg a = 16
Leb b = x
Plug these values into the above formula and solve for x:
c² = a² + b²
25² = 16² + x²
625 = 256 + x²
x² = 625 - 256
x² = 369
Take the square root( we use the positive value because its dimension ).
x = √369
x = 3√41
Therefore, the value of x is 3√41.
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What is the inverse of the following conditional statement? "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle." If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle. If the polygon is a triangle, then the sum of the interior angles of the polygon is not more than 180°. If the sum of the interior angles of a polygon is equal to 180°, then the polygon is a triangle. If the polygon is not a triangle, then the sum of the interior angles of the polygon is more than 180°.
The inverse of the original statement is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
The inverse of the conditional statement "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle" is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
To find the inverse, we need to negate both the hypothesis and the conclusion of the original statement.
The hypothesis of the original statement is "the sum of the interior angles of a polygon is more than 180°". To negate this, we say "the sum of the interior angles of a polygon is not more than 180°".
The conclusion of the original statement is "the polygon is not a triangle". To negate this, we say "the polygon is a triangle".
In summary, the inverse of the original statement is "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
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Find the area of the shaded region
Answer:
17.5
Step-by-step explanation:
The triangle is an equilateral triangle since all sides are equal
Area of a equilateral triangle is:
[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]
[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]
the sde of the square = diameterof the circle(d)
d = 6
r = d/2 = 3
ar(circle) = πr²
= π * 3²
= 9π
= 9*22/7
= 198/7
ar(shaded region) = ar(circle)-ar(triangle)
[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]
= 17.5
number 33!!!! this is a test !!!
33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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HELP I DONT NOW WHICH ONE IT IS?
The correct statement is the first one:
f(0) = 2
g(-2) = 0
Which statement is true about the two graphs?Here we can see the graph of two quadratic equations.
The orange one is g(x), and we can see that it has the vertex at (-2, 0).
And the blue one is f(x), we can see that the vertex is at (2, 0)
From, that, we coclude that:
g(-2) = 0
f(2) = 0
We also can see that the two have the sa,me y-intercept (0, 2), so:
f(0) = g(0) = 2
Then the correct statement is the first one:
f(0) = 2
g(-2) = 0
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ELEVEN LIONS FOUR CATS, AND SEVEN CROWS
HAVE A TOTAL OF:
Answer:
23 Heads or Legs
A parabola can be drawn given a focus of ... 100pts
Answer:
[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]
[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]
Step-by-step explanation:
The given directrix of the parabola is x = -2, which is a vertical line.
The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.
The standard form of a horizontal parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the focus is (-4, -7), then:
[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]
As the directrix is x = -2, then:
[tex]h - p=-2[/tex]
To find the value of h, sum the equations involved h and p to eliminate p:
[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]
To find the value of p, substitute the found value of h into one of the equations:
[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]
Therefore, the values of h, k and p are:
h = -3k = -7p = -1The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.
The parabola has a vertex at (-3, y), has p-value of 1 and it equation is
(x + 3)² = 4y.
What is the equation of the parabola?To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given:
Focus: (-4, -7)
Directrix: x = -2
1. Finding the vertex:
Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.
Therefore, the vertex of the parabola is (-3, y).
2. Finding the p-value:
The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.
Therefore, the value of "p" is 1.
3. Writing the equation of the parabola:
Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:
(x - h)² = 4p(y - k)
(x - (-3))² = 4(1)(y - y)
Simplifying, we get:
(x + 3)² = 4(y - y)
(x + 3)² = 4y
So, the equation of the parabola is (x + 3)² = 4y.
The vertex of the parabola is (-3, y) and the p-value is 1.
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The ratio of the length to the width of a rectangle is 3:2. If the perimeter of the rectangle is 40, what is the length of the rectangle?
Answer:
Step-by-step explanation:
Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:
P = 2(3x + 2x)
40 = 2(5x)
Now, let's solve for x:
40 = 10x
x = 40/10
x = 4
Now that we have the value of x, we can find the length of the rectangle:
Length = 3x = 3(4) = 12
Therefore, the length of the rectangle is 12.
In a sample of 5,000 students , the mean GPA is 2.80 and the standard deviation is 0.35. Assume the distribution to be normal.
How many students score below 2.60?
In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.
To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.
First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.
Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.
To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.
Since the number of students must be a whole number, we round down to 1428 students.
Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.
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A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)
Given the sequence 9/8, 3/4, 1/2,...,8/81 is the geometric sequence. Find the common ratio and the number of all terms of this sequence.
Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
As we know that,
Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.
So, r= (n+1)th term / nth term
where r ⇒ common ratio
(n+1)th term⇒ succeeding term
nth term⇒ preceding term
According to the given question, r = (9/8) / (3/4)
r = (2/3)
We also know,
Any term of a G.P. [nth term] can be obtained by the formula:
Tₙ= a[tex]r^{n-1}[/tex]
where, Tₙ= nth term
a= first term of G.P.
r=common ratio
Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.
Tₙ= a[tex]r^{n-1}[/tex]
⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])
⇒ (64/729)= ([tex]2/3^{n-1}[/tex])
⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])
⇒ n-1 = 6
⇒ n = 7
∴ The total number of terms in G.P. is 7.
Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.
Explanation:The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.
So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.
To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.
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a house is covers by a rectangle of ground 15.7m by 12.3m on the plan of the house the length of the rectangle is 78.5cm what is the scale of the plan in form 1:n ? find width if the house on the plan
The width of the house on the plan is 0.615 meters.
To find the scale of the plan in the form 1:n, we can compare the measurements on the plan to the actual measurements of the house.
Length of the rectangle on the plan = 78.5 cm
Actual length of the house = 15.7 m
We need to convert the actual length of the house to the same unit as the length on the plan, which is centimeters.
1 meter = 100 centimeters
So, the actual length of the house in centimeters = 15.7 m [tex]\times[/tex] 100 cm/m = 1570 cm
Now, we can find the scale of the plan by dividing the length on the plan by the actual length of the house:
Scale = Length on the plan / Actual length of the house
= 78.5 cm / 1570 cm
Simplifying this fraction, we get:
Scale = 1/20
Therefore, the scale of the plan is 1:20.
To find the width of the house on the plan, we can use the same scale.
Width of the house in actual measurements = 12.3 m.
Width of the house on the plan = (Width of the house in actual measurements) / Scale
= 12.3 m / 20
= 0.615 m.
So, the width of the house on the plan is 0.615 meters.
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José encontró un álbum de fotos del abuelo cuando tenía nueve años si el álbum tenía 108 páginas cuantas veces se habría es que se habría escrito la cifra nueve para enumerar todo el libro
The total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
To determine how many times the digit "9" would have been written to number all the pages of the photo album, we need to analyze the numbering pattern.
Since the album has 108 pages, we can observe that the numbers 1 to 9 are repeated 12 times (1-9, 10-19, 20-29, ..., 90-99) to cover the first 99 pages. Each repetition consists of ten numbers, and the digit "9" appears once in each repetition.
So, the digit "9" would have been written 12 times for the numbers 9, 19, 29, ..., 89 and 99.
However, we have an additional 9 pages to consider, which are 100, 101, 102, ..., 108. Each of these pages contains a single "9" in its numbering.
Therefore, the total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.
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Question 2 (1 point)
Which one of the following is true of the mean?
1) one of the less common averages
2) equals some whole number
observations must be ordered from least to most before calculating the
3)
mean
4) equals the sum of all observations divided by the number of observations
The correct statement about the mean is:
The mean equals the sum of all observations divided by the number of observations.
The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.
To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.
The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.
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Where will the hand of a clock stop if it
(a) starts at 12 and makes 1/2 of a revolution,clockwise?
(b) starts at 2 and makes 1/2 of a revolution,clockwise?
(c) starts at 5 and 1/4 of a revolution,clockwise?
(d) starts at 5 and makes 3/4 of a revolution,clockwise?
(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.
(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.
(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.
(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.
To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.
(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.
This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.
(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.
Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.
(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.
A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.
(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.
A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.
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What is the units digit of 2013 to the power
2013?
Step-by-step explanation:
a number consists of digits in the place of certain values of the powers of 10.
2013 consists of a digit 2 in the thousands units position.
of a digit 0 in the hundreds units position.
of a digit 1 in the tens units position.
and of a digit 3 in the (single) units position.
so, to which power do we need to have this 3 ?
I think you made a mistake there. you say we need it to the power of 2013 ?
3²⁰¹³ = 2.786671338...e960 =
= 2.786671338... × 10⁹⁶⁰
The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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1cm on a picture of a swimming pool represents 1200cm of the actual swimming pool. The length of the pictured swimming pool is 4.5cm and the width is 3cm. What is the perimeter of the actual swimming pool? Express your answer in meters.
Answer:
180 meters
Step-by-step explanation:
To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.
Length of actual swimming pool = 4.5 cm × 1200 cm = 5400 cmWidth of actual swimming pool = 3 cm × 1200 cm = 3600 cmPerimeter of actual swimming pool = (5400 cm + 3600 cm) × 2 = 18000 cm.Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:
100cm = 1mNow we can divide 18000 by 100:
18000 cm ÷ 100 = 180 m
Therefore, the perimeter of the actual swimming pool is 180 m.