All four angles of the rhombus are 20, 160, 20, and 160 degrees.
What is meant by diagonal of an angle ?Diagonals are the parts of a shape, in geometry, a diagonal is a line that join two vertices of a polygon or a solid shape , whose vertices are not on the same edge. In general, a diagonal is called as a sloping line or the slant line, that connects to the vertices of a shape.
According to question a rhombus , all four sides are congruent and opposite angles are equal. Let's call the rhombus ABCD, where AB, BC, CD, and DA are the four sides, and AC and BD are the diagonals.
If one of the angles formed by diagonals and adjacent sides is 20 degrees, let's say that angle is ABD. We can draw a line from point A to point C, which will divide the rhombus into two congruent triangles, ABC and ACD.
Since triangle ABC is isosceles, with sides AB = BC, angles ABC and BCA are equal. Similarly, in triangle ACD, angles ACD and CDA are equal.
∴ angles ABD and CDA are adjacent angles formed by intersecting lines, they must add up to 180 degrees. Therefore, angle CDA is 160 degrees.
If triangles ABC and ACD are congruent, angle CAD is also 20 degrees.
Now we can use the fact that opposite angles in a rhombus are equal. Angles BCD and ABD are opposite angles, so angle BCD is also 20 degrees. Similarly, angles BAC and ADC are opposite angles, so angle BAC is also 160 degrees.
Therefore, all four angles of the rhombus are 20, 160, 20, and 160 degrees.
Complete question If one of the angles formed by diagonals and adjacent sides. of Is 20, all four angles of the a rhombus are.
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The lodge has 420 skis. Predict the number of skis that are likely to be defective.
A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.
It is assumed that there are 80 skis, four of which are faulty.
As a result, the total number of outcomes is 80.
Positive outcomes = 4
Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.
[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis
= 4 / 80
= 1 / 20
=0.05
Skis will be discovered in 5% of cases.
So, the event of choosing a defective is 4 / 80.
If the total number of skis is 420, then the number of defective skis will be:
4 / 80 × 420
= 1/20 × 420
= 21
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Correct question:
A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.
what is the measure of an angle if it is 590 less than six times its own supplement
This is a word problem involving supplementary angles. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.
Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:
x=6(180−x)−590
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
xx7xxx=6(180−x)−590=1080−6x−590=490=7490=70
Therefore, the measure of the angle is 70°.
Find the next three numbers in the pattern: 2,0,6,−4,10,−8,
The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.
To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.
The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.
The pattern is as follows : 2 - (2×1) = 0,
0 + (2×3) = 6,
6 - (2×5) = -4,
-4 + (2×7) = 10,
10 - (2×9) = -8,
Using this rule, we can find the next three numbers in the pattern as follows:
Add 22 because : -8 + (2×11) = 14,
Subtract 26 because : 14 - (2×13) = -12,
Add 30 , because : -12 + (2×15) = 18,
Therefore, the next three numbers in the pattern are 14, -12, and 18.
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100 Points!!! Algebra question. Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Please show as much work as possible. Photo attached. Thank you!
The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at;
-3, f(-3) = 390 and at 4, f(4) = 537
What is a functionA function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
By substitution:
For x = -3;
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3
f(-3) = 243 + 108 + 27 + 15 - 3
f(-3) = 390
For x = 4;
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
f(4) = 3(256) - 4(64) + 3(16) - 20 - 3
f(4) = 768 - 256 + 48 - 20 - 3
f(4) = 537
Therefore, the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537 respectively.
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The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79
,
73
,
72
,
70
,
72
,
66
,
81
,
75
79, 73, 72, 70, 72, 66, 81, 75
What is the median high daily temperature, in degrees Fahrenheit, in the city?
For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.
In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:
The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}
There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.
In this case, the temperature of the fourth day is 72, and fifth day is 73,
The average will be = (72+73)/2 = 72.5,
Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.
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The given question is incomplete, the complete question is
The data set shown below represents the distribution of daily high temperatures in a city for 8 days.
79,73,72,70,72,66,81,75.
What is the median high daily temperature, in degrees Fahrenheit, in the city?
Jennifer deposits money into a bank account. The amount of money in her account is measured in dollars, and can be modelled by the function A(m)= 1750(1.025)^m, where m is the number of months since the initial deposit.
What is the percent change in Jennifer's account balance each month? Is it increasing or decreasing? Justify answer.
a) The percent change in Jennifer's account balance each month is 2.5%.
b) Based on the future value function, A(m)= 1750(1.025)^m, the account balance is increasing because the growth factor is 1.025 and not less than 1.
What is a growth function?A growth function is a mathematical equation that shows a constant rate in increase or growth in value of the dependent variable.
A growth function is modeled by a growth factor greater than 1 while a decay function shows a decay.
Percentage change = 2.5% (1.025 - 1)
2.5% = 2.5 ÷ 100 = 0.025
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the set of five number each of which is divisble by 3
Answer:
Here's a set of five numbers, each of which is divisible by 3:
{ 3, 6, 9, 12, 15 }
All the numbers in this set are multiples of 3, so they are all divisible by 3.
This is so hard. Can you help me with this?
Answer: 70, 6
Step-by-step explanation:
(a) For <F that is the same as <D. The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same
All of the angles are = 180 if you subtract <E, you are left with 140 to be split between <F and <D
<F= 70
(b) all of the sides are the same because all the angles are the same
so AB=6
If $4,500 is invested at an interest rate of 5.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 4 years
(b) 8 years
(c) 12 years
a) The value of the investment after 4 years is $5,544.90.
b) The value of the investment after 8 years is $6,849.42.
c) The value of the investment after 12 years is $8,453.35.
The formula for calculating the value of an investment that is compounded continuously is given by:
A = [tex]Pe^{(rt)[/tex]
where A is the final value of the investment, P is the initial investment amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time period in years.
(a) To find the value of the investment after 4 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05254)[/tex]
A = 4500[tex]e^{0.21[/tex]
A = 45001.2322
A = $5,544.90
(b) To find the value of the investment after 8 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.05258)[/tex]
A = 4500[tex]e^{0.42[/tex]
A = 45001.5221
A = $6,849.42
(c) To find the value of the investment after 12 years, we can substitute the given values in the formula as follows:
A = 4500[tex]e^{(0.052512)[/tex]
A = 4500[tex]e^{0.63[/tex]
A = 45001.8785
A = $8,453.35
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2. If 15% of the first digit equals 21% of the second digit, then what percentage of the second digit equals 25% of the first digit?
Answer:
35%
(I replaced the 1st digit by a and the second digit by b)
If angle 3=61, what should angle 1 and angle 2 be?
Answer:
Step-by-step explanation:
so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)
Graph the function f(x) = 14(0.87)x. Does this function show growth or decay? What is the equation of the asymptote? Growth; y = 0 Growth; y = 14 Decay; y = 0 Decay; y = 14
The truth statements about the function f(x) = 14(0.87)^x is Growth; y = 0
Does the function show growth or decay?From the question, we have the following parameters that can be used in our computation:
f(x) = 14(0.87)^x
An exponential function is represented as
y = ab^x
Where
a = initial value
b = growth/decay factor
In this case, the exponential function is a decay function
This means that
The value of b is less than 1 i.e.
b = 0.87 and 0.87 < 1
Hence, the function is a decay function
What is the equation of the asymptote?Recall that
f(x) = 14(0.87)^x
So, we have
y = 0 as the the equation of the asymptote
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What is the measure (in radians) of central angle θ in the circle below?
Enter an exact expression. (in radians)
HELP NEEDED ASAP
The measure (in radians) of central angle θ in the circle below is π/3.
We have,
radius = 3 cm
Arc length = π
We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:
s = r Ф
Now,
π = 3 x Ф
Ф = π/3
Thus,
The measure (in radians) of central angle θ in the circle below is π/3.
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Which choice is the correct graph of |x|< 3
The graph that shows the solution set for the given inequality is the one in option B.
Which one is the graph of the given inequality?Here we want to identify the graph of the inequality:
|x| ≤ 3
So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.
(We use closed circles because these values are also solutions for the inequality).
With that in mind, we can see that the correct option in this case will be graph B.
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P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
What is P(J)?
O 0.1105
O 0.8143
O 0.8895
O 0.1857
The conditional value probability is solved and P ( J ) = 0.1105
Given data ,
P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
We can use Bayes' theorem to find P(J):
P(J | K) = P(K | J) * P(J) / P(K)
0.35 = 0.95 * P(J) / 0.3
0.35 * 0.3 = 0.95 * P(J)
0.105 = 0.95 * P(J)
P(J) = 0.105 / 0.95
P(J) = 0.1105
Hence , the probability is P ( J ) = 0.1105
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Create a matrix for this linear system: 3x+2y+z = 26 X-4y = -11 2x+z = 13 The determinant of the coefficient matrix is _______. x = y = z =
Answer:
[tex]\mathrm{Matrix \: Form:}[/tex]
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
[tex]\mathrm{Determinant\; of \;coefficient \;matrix = - 6}[/tex]
Step-by-step explanation:
The system of linear equations provided in the question:
[tex]\begin{aligned}3x+2y+z &= 26\\ x-4y&=-11\\ 2x+z&=13\\\\\end{aligned}[/tex]
can be represented in matrix form as
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\begin{pmatrix}x\\ y\\ z\end{pmatrix} = \begin{pmatrix}26\\ -11\\ 13\end{pmatrix}[/tex]
The coefficient matrix is
[tex]\begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
The determinant of this matrix can be obtained by the expansion formula:
[tex]\det \begin{pmatrix}a&b&c\\ \:d&e&f\\ \:g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ \:h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ \:g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ \:g&h\end{pmatrix}[/tex]
Therefore
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}[/tex]
[tex]= 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}[/tex]
[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]
[tex]\det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix} = \left(-4\right)\cdot \:1-0\cdot \:0 = -4[/tex]
[tex]\det \begin{pmatrix}1&0\\ 2&1\end{pmatrix} = 1\cdot \:1-0\cdot \:2 = 1[/tex]
[tex]\det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix} = 1\cdot \:0-\left(-4\right)\cdot \:2 =8[/tex]
Finally,
[tex]det \begin{pmatrix}3&2&1\\ 1&-4&0\\ 2&0&1\end{pmatrix}\\\\\\ = 3\cdot \det \begin{pmatrix}-4&0\\ 0&1\end{pmatrix}-2\cdot \det \begin{pmatrix}1&0\\ 2&1\end{pmatrix}+1\cdot \det \begin{pmatrix}1&-4\\ 2&0\end{pmatrix}\\\\\\= 3\left(-4\right)-2\cdot \:1+1\cdot \:8\\\\= -12 - 2 + 8\\\\= -6[/tex]
Assignments...
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Khan Academy
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
fy=
=−x+2
Get Al Guide
y = 3x -4
Donate
The solution of the given system of equations is (1, 2.5)
How to explain the equationFrom the graph attached, it van be seen that two intersecting lines represent the system of equations.
And the solution of the system of equations is a common point where these lines intersect.
The graph shows both the line are intersecting each other at (1, 2.5).
Therefore, the solution of the given system of equations will be (1, 2.5).
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The whole page Tysm plsssssss step by step btw
The sum of all the pets in the list is 11.
The average number of pets that the students own is 1.375.
How to calculate the sumIt should be noted that to find the sum of all the pets in the list, we simply add up all the values:
0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11
Therefore, the sum of all the pets in the list is 11.
Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:
11 ÷ 8 = 1.375
Therefore, the average number of pets that the students own is 1.375.
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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.
0 1 2 3 1 2 0 2
What is The sum of all the pets in the list
What is the average number of pets that the students own
Jaswat set out to walk a distance of 12 Km. After walking for 1 1/2 hours at a speed of
6 Km/h, he had to slow down to steady pace of 4 Km/h , which he maintained till the
end of the journey. How long did he take to complete the journey?
Answer: 2 hours 15 minutes
Step-by-step explanation:
To solve this problem, we need to use the formula:
distance = speed x time
First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:
distance = speed x time
distance = 6 Km/h x 1.5 h
distance = 9 Km
So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.
Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:
distance = speed x time
3 Km = 4 Km/h x time
time = 3 Km / 4 Km/h
time = 0.75 hours = 45 minutes
Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.
50 Points! Multiple choice Algebra question. State the number of real zeros for the function whose graph is shown. Photo attached. Thank you!
The number of real zeros for the function whose graph is shown include the following: D. 0.
What is a polynomial function?In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.
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tamara plays video games for the same amount of time each day. in 4 days she played video games for 48 minutes in 9 days how many minutes did she play video games
Answer:
Step-by-step explanation:
Its simple, you need to find x
4 days the same amount of time (x) gives 48 min
4x = 48
x = 48/4
x = 12
then to get the amount of minutes in 9 days it would be:
9x=days
9(12)=108
the answer would be 108 min
Answer:
108 mins
Step-by-step explanation:
48 mins/4 days = x mins/9 days
4x= 432
x=108 mins
QUESTION 1
Joe's Pizza Company faces a demand for its pizzas which obeys the "law of demand." This means if Joe lowers the price he charges
per pizza
His profit will rise.
He will sell more pizzas.
His profit will fall.
He will sell fewer pizzas.
If Joe lowers the price he charges per pizza, he will sell more pizzas. option B
Why would he sell more?To sell more pizza, Joe must decrease the price he charges per unit. The law of demand dictates that when a product's cost decreases, its quantity demanded rises resulting in an increased sales volume.
It follows then that if Joe reduces his pizza prices more people will be inclined to purchase it creating this increase in sales . Nonetheless, whether Joe’s profit will rise or diminish depends on the extent of the rise in sales compared to the lowering of the price.
Even if there is a reduction in the price of every pizza, if the resultant sales volume is significant enough, Joe’s profit margin could still experience a positive turn.
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Please reply me as soon as possible with step by step answer for this
The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
What is the length of the curve?To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:
y' = -4
Then, we can use the arc length formula:
L = ∫[a,b] √(1 + (y')^2) dx
where a and b are the limits of integration. In this case, a = -2 and b = 2.
L = ∫[-2,2] √(1 + (-4)^2) dx
= ∫[-2,2] √(17) dx
= √(17) * [x]_(-2)^(2)
= 4√(17)
So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).
To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:
L = √((0.75 - (-2))^2 + (1 - 13)^2)
L = √(18.25 + 144)
L = √(162.25)
L = 4√(17)
This matches our previous answer, so we can be confident that the length of the curve is 4√(17).
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9. Economists in the country of Flatland, a closed economy, have collected the following information about their economy for a particular year: Y=15,000; C=9,000; T=3,000; G=3,600. The economists also estimate that the investment function is I=3,900-100r, where r is the country’s real interest rate, expressed as a percentage.
Calculate private saving, public saving, national saving, investment, and the equilibrium real interest rate. Does the government of Flatland have a budget surplus or budget deficit?
Answer:
Private saving (Sprivate) is equal to disposable income minus consumption:
Sprivate = Y - T - C = 15,000 - 3,000 - 9,000 = 3,000
Public saving (Spublic) is equal to government revenue minus government spending:
Spublic = T - G = 3,000 - 3,600 = -600
National saving (S) is equal to the sum of private and public saving:
S = Sprivate + Spublic = 3,000 - 600 = 2,400
Investment (I) is given by the investment function:
I = 3,900 - 100r
Equating investment to national saving gives:
I = S
3,900 - 100r = 2,400
Solving for r:
r = 15%
Therefore, the equilibrium real interest rate is 15%.
Substituting r = 15% into the investment function gives:
I = 2,400
Therefore, investment is 2,400.
Finally, to determine if the government has a budget surplus or deficit, we need to calculate the government's budget balance, which is equal to government revenue minus government spending:
Budget balance = T - G = 3,000 - 3,600 = -600
Since the budget balance is negative, the government of Flatland has a budget deficit.
Write a slope-intercept equation for a line passing(3,-2) through the point that is parallel to the line 3X+4Y= 9. Then write a second equation for a line passing through the point (3,-2) that is perpendicular to the line 3X+4Y= 9.
Assistance needed pls and thanks
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)
[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)
[tex]\vec a + \vec b[/tex] = (3, 1).
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ibrahim drew the graph below.
which of the following statements best describes the graph?
Answer:
B
Step-by-step explanation:
This is a linear function.
:D
Put the expressions in order from the least to greatest
Step-by-step explanation:
[tex] { ({4}^{ - 4} )}^{3} \\ = {4}^{ - 12} [/tex]
[tex] \frac{ {4}^{15} }{ {4}^{5} } \\ = {4}^{10} [/tex]
[tex] {4}^{ - 5} \times {4}^{ - 4} \\ = {4}^{ - 9} [/tex]
[tex] \frac{1}{ {4}^{ - 12} } \\ = {4}^{12} [/tex]
least to greatest
[tex]1)\: {4}^{ - 12} \\ 2) \: {4}^{ - 9} \\ 3) \: {4}^{10 } \\ 4) \: {4}^{12} [/tex]
#CMIIWA research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
The appropriate statistic for testing the null hypothesis is given as D (-2.20/0.07)
How tp get the statisticCoefficient for slope variable (Exercise time) = -2.20
Standard error of coefficient = 0.07
Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.
Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07
Therefore its correct answer is D (-2.20/0.07)
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You want to determine the number of students in your school who have visited a public library. You survey 30 students at random. Twenty-four have visited a public library, and six have not. So, you conclude that 80% of the students in your school have visited a public library.
Determine whether the conclusion is valid
Answer: e
Step-by-step explanation:
Answer:Valid
Step-by-step explanation: