Answer:
Step-by-step explanation:
If y varies directly as x, it means that y is directly proportional to x, and we can express this relationship using a proportionality constant k:
y = kx
To find the value of k, we can use the given information that y = 2 when x = 3:
2 = k(3)
Solving for k, we get:
k = 2/3
Now that we know the value of k, we can use the formula to find y when x = 1:
y = (2/3)x
y = (2/3)(1)
y = 2/3
Therefore, when x = 1, y = 2/3.
3 + 1 + 2 − 7 = + 22
Answer: The answer is false
Answer:
False
Step-by-step explanation:
If you were asking true or false it is false
Find the missing angle:
If f(x) is defined as follows, find (a) f(-3), (b) f(0), and (c) f(4).
x²
if x < 0
if x = 0
3x + 3 ifx>0
f(x) = 0
(a) f(-3)= (Simplify your answer.)
THE
For the given question the values,
f(-1) = 1f(0) = 0f(3) = 13Given value of the function when the condition for x is less than '0' is =
f(x) = x² for x < 0
The value of the function when the condition x is equals to '0' is =
f(x) = 0 for x = 0
The value of the function when the condition x is greater than '0' is =
f(x) = 3x + 4 for x > 0
From the above information,
To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1
To find f(0) we have to use x value as 0. So, f(0) = 0
To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.
From the above analysis, we find the values of f(-1), f(0), and f(3).
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f(x)=2x³-5x²
g(x)=2x-1
Find (f- g)(x)
Answer:
2x³-5x² - 2x + 1
Step-by-step explanation:
We are given
f(x) = 2x³ - 5x²
g(x) = 2x - 1
and asked to find (f - g)(x)
(f - g)(x) is nothing but f(x) - g(x)
(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)
= 2x³-5x² - 2x + 1
The question is done below has square roots and exponents. Pretty easy.
Answer: D. -1
Step-by-step explanation:
Your equation:
[tex]\sqrt[4]{(\sqrt[3]{64}) ^{2} } =(\frac{1}{2} )^{x}[/tex] >We are going to work from the inside first then out
The cube root of 64 is 4 because 4*4*4=64
[tex]\sqrt[4]{(4) ^{2} } =(\frac{1}{2} )^{x}[/tex] > 4² = 4*4=16
[tex]\sqrt[4]{(16) } =(\frac{1}{2} )^{x}[/tex] > the 4th root of 16 is 2 because 2*2*2*2=16
[tex]2 =(\frac{1}{2} )^{x}[/tex] > if you have the same bases you can set the
exponents equal. They are not the same but we
are going to make them the same.
[tex]2^{1} =(\frac{1}{2} )^{x}[/tex] > 2 is the same as 2^1, i can make the bases the
same if I can make the 2 a reciprocal. That
happens when I take the negative exponent of the
number
[tex](\frac{1}{2} )^{-1} =(\frac{1}{2} )^{x}[/tex] >Now that my bases are the same, I can make the
exponents =
-1 = x
The following transactions are taken from the record of ABC
(a) Commenced business with cash of Rs. 1,00,000 and Machine of Rs. 50,000.
(b) Purchased goods for cash Rs. 30,000 and credit Rs. 10,000.
(c) Sold goods for cash Rs. 25,000 and credit Rs. 15,000.
(d)
Goods taken by the owner for private use Rs. 2,000.
Cash paid to creditors Rs 8,000.
(e)
(f) Cash received from debtors Rs. 14,500 in full settlement.
(g) Received a loan of Rs. 5,000 from Mr. Dipendra.
(h) He introduced additional capital Rs. 40,000.
Required: Accounting equation
Ans: A = Rs. 1,94,500, C= Rs. 1,87,500, L = Rs. 7,000
The accounting equation is:
Assets = Rs. 2,19,500
Liabilities = Rs. 1,000
Capital = Rs. 2,10,500
How to determine the accounting equationThe accounting equation is:
Assets = Liabilities + Capital
(a) Commenced business with cash of Rs. 1,00,000 and Machine of Rs. 50,000.
Assets = Cash + Machine = Rs. 1,00,000 + Rs. 50,000 = Rs. 1,50,000
(b) Purchased goods for cash Rs. 30,000 and credit Rs. 10,000.
Assets = Cash + Inventory = Rs. 1,30,000
Liabilities = Accounts Payable = Rs. 10,000
(c) Sold goods for cash Rs. 25,000 and credit Rs. 15,000.
Assets = Cash + Accounts Receivable + Inventory = Rs. 1,70,000
Liabilities = Accounts Payable = Rs. 10,000
(d) Goods taken by the owner for private use Rs. 2,000.
Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,68,000
(e) Cash paid to creditors Rs 8,000.
Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,60,000
Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000
(f) Cash received from debtors Rs. 14,500 in full settlement.
Assets = Cash + Inventory - Drawings = Rs. 1,74,500
Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000
Capital = Rs. 1,70,500
(g) Received a loan of Rs. 5,000 from Mr. Dipendra.
Assets = Cash + Inventory - Drawings = Rs. 1,79,500
Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000
Capital = Rs. 1,74,500
(h) He introduced additional capital Rs. 40,000.
Assets = Cash + Inventory - Drawings = Rs. 2,19,500
Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000
Capital = Rs. 2,10,500
Therefore, the accounting equation is:
Assets = Rs. 2,19,500
Liabilities = Rs. 1,000
Capital = Rs. 2,10,500
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5. The population, P, of a city has grown according to the mathematical model P = 50 000(1.15), where t
is the number of years since 2005.
Using a graphing tool or by hand answer the questions below.
a) What was the population of the town in 2005?
I
b) In what year will the population exceed 100 000?
Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.
Step-by-step explanation: a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:
P = 50,000(1.15)^0 = 50,000
Therefore, the population of the town in 2005 was 50,000.
b) We need to find the value of t when the population P exceeds 100,000:
100,000 = 50,000(1.15)^t
Divide both sides by 50,000:
2 = 1.15^t
Take the natural logarithm of both sides:
ln 2 = ln (1.15^t)
Apply the power rule of logarithms:
ln 2 = t ln 1.15
Divide both sides by ln 1.15:
t = ln 2 / ln 1.15
Using a calculator, we get:
t ≈ 10.73
Please help!!
If someone could explain how to solve this question I would appreciate it!
2430+15√2=
Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.
Using a calculator, you can directly evaluate the expression to get:
2430 + 15√2 ≈ 2462.11
Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:
2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21
Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.
Step-by-step explanation:
The scale of this blueprint of an art gallery is 1 in 48 ft. find the actual lengths of the following walls.
The calculated values of the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft
Finding the actual lengths of the walls.From the question, we have the following parameters that can be used in our computation:
Scale of blueprint = 1 in : 48 ft
This means that
Scale = 48 ft/1in
Calculating the actual lengths of the walls, we have
AB = 3in * 48 ft/1in
AB = 144 ft
CD = 6in * 48 ft/1in
CD = 288 ft
EF = 11in * 48 ft/1in
EF = 528 ft
FG = 5in * 48 ft/1in
EF = 240 ft
Hence, the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft
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If your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
SUBMIT
Answer:
Total amount of becomes after 16 year is $93649 .
What's the difference between $4 and 36 cents
Answer:
364 cents or $3.64
Step-by-step explanation:
We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.
400 - 36 = 364
Difference is 364 cents or $3.64
16
Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
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m. All rights reserved.
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Arc
Length
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A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.
How to calculate the length of the arc?In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):
Arc length = 2πr × θ/360
In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.
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Find m/_I. I need help on solving this problem please?
Answer:
∠ I = 60°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan I = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{HJ}{IJ}[/tex] = [tex]\frac{3\sqrt{30} }{3\sqrt{10} }[/tex] = [tex]\frac{\sqrt{30} }{\sqrt{10} }[/tex] = [tex]\sqrt{\frac{30}{10} }[/tex] = [tex]\sqrt{3}[/tex] , then
∠ I = [tex]tan^{-1}[/tex] ([tex]\sqrt{3}[/tex] ) = 60°
Answer:
60°
Step-by-step explanation:
You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
In this triangle, ...
tan(I) = (3√30)/(3√10) = √(30/10) = √3
Then the angle is ...
I = arctan(√3) = 60°
The measure of angle I is 60°.
__
Additional comment
The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:
30°-60°-90° triangle has side ratios 1 : √3 : 2
45°-45°-90° triangle has side ratios 1 : 1 : √2
Of course, side lengths are in the same order as their opposite angles.
The mnemonic SOH CAH TOA can help you remember the necessary relationships:
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentWrite an Equation for the ellipse. The center is (1, -3).
The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.
How to define the standard form of the equation of an ellipse
In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a - Length of the major semiaxis.b - Length of the minor semiaxis.If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:
(x - 1)² / 16 + (y + 3) / 9 = 1
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NEED HELP ASAP PLS AND THX PIC IS ATTACHED
Step-by-step explanation:
You would need a calculator in the degree function I believe, but basically for Number 1,
you would set it up in calculator as Sin ^-1 (6/9) or write it down as Sin(X)=(6/9)
2. would be Cos(45)= (X/4) meaning you'd do Cos(45) times 4.
3. is basically Tan(60) =(x/4) so it's basically Tan(60) times 4.
make sure your calculator is in degree mode ? Sorry, I don't remember if you need to be in radiant or degree mode. I can comment or make an edit when I remember.
show that f= 16 is
R
equivalent to
fpm = 12
RPM in fluid flow through porous media
Lara chooses a number less than 20
She divides it by 2 and then adds 6
She then divides this result by 3
Her answer is 4.5
What was the number she started with?
Working backward, the number that Lara started with in performing the mathematical operations was 15.
How the number is determined:We can use mathematical operations to determine the initial number that Lara started with.
Mathematical operations include addition, subtraction, division, multiplication, etc.
Let the number that Lara started with = x
x < 20
x ÷ 2 + 6 = y
y ÷ 3 = 4.5
y = 13.5 (4.5 x 3)
x ÷ 2 + 6 = 13.5
x ÷ 2 = 7.5
x = 15 (7.5 x 2)
Thus, Lara started performing the mathematical operations with 15 and got a final result of 4.5.
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how many teams completed the escape room in 45 minutes or less
The answer to the question about how many teams completed the escape room in 45 minutes or less is 6.
What is a Dot Plot?A dot plot is a type of chart used to display the distribution of a dataset. It is also known as a dot chart, strip plot, or dot graph. In a dot plot, each data point is represented by a dot placed along a horizontal or vertical axis.
Dot plots are useful for showing the distribution of a small to moderate-sized dataset, and are especially helpful when you want to compare the distribution of two or more datasets side by side. They are also useful for identifying outliers or gaps in the data
How did we find this answer?If we count the amount of dots on 45 and before 45 and add them up, the answer is 6
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What is the numerical expression that represents the sun of eight squared and thirty two
The numerical expression that represents the sum of eight squared and thirty two will be 96.
A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
The numerical expression that represents the sum of eight squared and thirty two is
= 8² + 32
= 64 + 32
= 96.
The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.
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The model shown below is a perfect cube with a volume of 27 cubic units. Which statement is true about all perfect cubes?
A. A perfect cube represents 3 times the area of a face of the cube.
B. A perfect cube represents the sum of 9 edge lengths of the cube.
C. A perfect cube represents the volume of a cube with equal integer side lengths.
D. A perfect cube represents the surface area of a cube with equal integer side lengths.
The correct statement which is true about all perfect cubes is,
⇒ A perfect cube represents 3 times the area of a face of the cube.
We have to given that;
The model shown below is a perfect cube with a volume of 27 cubic units.
Now, We can formulate;
⇒ V = 27 cubic units.
⇒ V = 3 × 9 cubic units.
⇒ V = 3 × 3² cubic units.
Thus, The correct statement which is true about all perfect cubes is,
⇒ A perfect cube represents 3 times the area of a face of the cube.
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A mathematics teacher wanted to see the correlation between test
scores and homework. The homework grade (x) and test grade (y) are
given in the accompanying table. Write the linear regression equation
that represents this set of data, rounding all coefficients to the nearest
hundredth. Using this equation, find the projected test grade, to the
nearest integer, for a student with a homework grade of 61.
Homework Grade (x) 72 53 90 77 82 74 78 74 83Test Grade (y)
75 39 81 70 83 78 75 70 85
Answer:
54
Step-by-step explanation:
You want the approximate test grade of a student with a homework grade of 61, using a linear regression equation for the given homework and test scores.
RegressionThe linear regression equation can be found using any of a number of calculators, apps, or spreadsheets. The attachment shows the equation is approximately ...
y ≈ 1.22x -20.01
For a homework score of 61, the expected test grade is ...
y = 1.22(61) -20.01
y ≈ 54
The student's projected test grade is 54.
__
Additional comment
If the regression coefficients are used to their full precision, the projected test score is about 54.6, which rounds to 55.
<95141404393>
Evaluate log_10^3.
a) 100
b) 1, 000
c) 9
d) 3
What are the period and amplitude of the function?
Answer:
period : π ; amplitude : 2
Step-by-step explanation:
Correct me if I'm wrong!!
Find the lengths of each triangle…
2x ft
6x ft
200ft
Answer:
[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]
[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]
Step-by-step explanation:
Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.
Pythagoras Theorem[tex]\large{\boxed{a^2+b^2=c^2}[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.From inspection of the given diagram:
a = 2xb = 6xc = 200Substitute these values into the formula and solve for x.
[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]
Substitute the found value of x into the expression for each side length.
[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]
[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]
Therefore, the exact side lengths of the given right triangle are:
[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]
The side lengths to the nearest hundredth are:
63.25 ft189.74 ft200 ftIn 1949, Jackie Robinson hit .342 for the Brooklyn Dodgers; in 1973, Rod Carew hit .350 for the Minnesota Twins. In the 1970s the mean batting average was
.261 and the standard deviation was .0317. Determine which
batting average was more impressive.
In 1973, the batting average of .350 of Rod Carew is more impressive as it has a higher z-score of 2.81
To establish which batting average was more spectacular, we must compare it to the mean and standard deviation of 1970s hitting averages. The case of Jackie Robinson,
z = (x - μ) / σ
z = (.342 - .261) / .0317
z = 2.56
For Rod Carew,
z = (x - μ) / σ
z = (.350 - .261) / .0317
z = 2.81
A higher z-score indicates a more impressive performance relative to the mean. As a result, Rod Carew's .350 batting average was more spectacular, as it had a higher z-score of 2.81 than Jackie Robinson's z-score of 2.56.
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I need the answers and a explanation if possible
Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.
How to explain the hypothesisNull Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.
Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.
The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.
For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.
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What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
Answer:
the surface area of the rectangular prism is 572cm².
Step-by-step explanation:
The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:
2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²
So the surface area of the rectangular prism is 572 square centimeters.
Add 2 1/3 + 4 5/8 writ your answer as a mixed number
Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.
Find the missing dimensions of each figure. Round your answer to the nearest tenth. PLEASE HELP
answer is : r=1.6 in since the volume of cylinder is :
[tex]\pi {r}^{2} h[/tex]
Question is in image
Answer:
366,699
Step-by-step explanation:
to solve this problem, we can use the following formula for exponential growth:
population = initial population x (1 + growth rate)^time
where the initial population is the current population, the growth rate is the rate of increase per year, and the time is the number of years.
Plugging in the given values, we get:
population = 300,000 x (1 + 0.02)^10
Simplifying, we get:
population = 300,000 x 1.02^10
Using a calculator, we get:
population ≈ 366,698.79
Rounding to the nearest whole number, we get:
population ≈ 366,699
The population in 10 years will be approximately 366,699