The measure of ∠STR in the isosceles triangle is 24°
What is an isosceles triangle?
A triangle having two sides of equal length is termed as an isosceles triangle. The base angles of an isosceles triangle are also equal in measure. The fact that the perpendicular bisector of the base and the angle bisector of the vertex angle are the same is another crucial characteristic of an isosceles triangle. We refer this as Isosceles Triangle Theorem.
What is the value of angle STR?
It is given that in isosceles triangle SQT,
∠STQ = 48°
Since, the line TR is the angle bisector of angle STQ, we have,
∠STR = ∠RTQ
And, ∠STR + ∠RTQ = ∠STQ
Let ∠STR be x, the, we get,
x + x = ∠STQ
⇒ 2x = 48°
⇒ x = 24°
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A golf club manufacturer measures the impact elasticity of a new material. This is done by randomly selecting a driver head made from the new material, firing a golf ball at it from an air cannon (under carefully controlled conditions), and making certain measurements of the ball's motion. These measurements are used to calculate a number called the coefficient of restitution of the driver head. Engineers use this procedure 30 times. The sample mean coefficient of restitution is 0.835. Calculate a 99% confidence interval for the true mean coefficient of restitution, assuming the population standard deviation of such coefficients is 0.019. Round your answers to the fourth decimal digit.
The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.
We have to find the confidence interval for the true mean coefficient of restitution.
We can easily find the confidence interval through the formula of margin of error.
Margin of error is the difference between the calculated values and the real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the z value of p value,
σ is population mean or sample mean,
n is the sample size.
In our problem the sample size is 30.
z value for the p value of 0.99 is 2.576.
Margin of error=2.576*0.019/[tex]\sqrt{30}[/tex]
=0.048944/5.4772
=0.0089
Upper level=mean +margin of error
=30+0.0089
=30.0089
Lower level=Mean-margin of error
=30-0.0089
=29.9911.
Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
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Please help question in the picture
Answer:
D
Step-by-step explanation:
D is correct because the sqrt of 91 is 9.5 and 9<9.5<10 makes absolute sense
C is not correct because the sqrt of 33 is 5.7 and 6<5.7<7 does not make sense
B is not correct because the sqrt of 13 is 3.6 and 4<3.6<5 does not make sense
A is not correct because the sqrt of 65 is 8.06 and 7<8.06<8 does not make sense
PLEASE HELP I NEED THIS SOON! The monthly revenue of a digital magazine from each user is represented by the function f(x) = 4x + 1. The monthly cost to provide the digital magazine to each user per month is represented by the function g(x) = x2. Which of the following evaluates the profit function for each user of the digital magazine after 2 months?
A (f • g)(2) = (4(2) + 1)(22) = (9)(4) = $36
B (f + g)(2) = (4(2) + 1) + 22 = 9 + 4 = $13
C (g − f)(2) = 22 − (4(2) + 1) = 4 − 9 = −$5
D (f − g)(2) = (4(2) + 1) − 22 = 9 − 4 = $5
Answer:
The answer is D(f-g)
Step-by-step explanation:
Profit minus expenses
Answer:
D
Step-by-step explanation:
The profit can be defined as (cost of production) - (revenue) and since the cost is defined as g(x) = x^2 and the revenue is f(x) = 4x+1. The profit can be defined as [tex](f-g) = (4x+1)-x^2 = -x^2+4x+1[/tex]. After 2 months you can calculate the profit by simply plugging in 2 as x. This gives you the equation: [tex](f-g) = (4(2) + 1) - 2^2 = 9-4 = 5\$[/tex]
if the reserve ratio is 50%, and $10,000 in new deposits is added to the banking system, how much of the new deposits is the bank required to keep on hand? (eco class
$5000
$500
$1500
$50
Step-by-step explanation:
5,000 by dividing 10.000
$5000 of the new deposits is the bank required to keep on hand.
The answer is option A.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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You have just started a colony on Mars. One of the biggest concerns for the colony is government. What is your colony going to do? You must discuss three topics. First, of the five government types discussed in the lesson, what type will you use to make sure your colony operates smoothly? Second, what powers will your government have, and what powers will the people living in the colony have? Third, explain why you believe the government type you choose is the best option for your colony. please help
Answer:
we will use democracy so that everyone gets a say in what happens to the colony, second the government will make the decisions and the people will provide options and different ideas, and i believe its the best type because everyone has a say in what happens and the government isn't too powerful and has as much power as the people do.
Step-by-step explanation:
please help me im in a rush
Answer:
[tex] \frac{x}{y} = \frac{10}{5} \\ = \frac{5}{1} [/tex]
1. •°• y is 5 times x
[tex] \frac{x}{y} = \frac{30}{5} \\ = \frac{6}{1} [/tex]
2. •°• y is 6 times x
[tex] \frac{x}{y} = \frac{56}{8} \\ = \frac{7}{1} [/tex]
3. •°• y is 7 times x
[tex] \frac{x}{y} = \frac{88}{11} \\ = \frac{8}{1} [/tex]
4. •°• y is 8 times x
[tex]2 \times \frac{7}{4} [/tex]
•°• y is 2 times x
[tex]5 \times \frac{7}{4} [/tex]
•°• y is 5 times x
[tex]8 \times \frac{7}{4} [/tex]
•°• y is 8 times x
[tex]11 \times \frac{7}{4} [/tex]
•°• y is 11 times x
Suppose that a box contains 8 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random with replacement. Define the random variable X X as the number of defective cameras in the sample. Write the binomial probability distribution for X X . Round to two decimal places. X X P ( X ) P(X) What is the expected value of X X ? Round to two decimal places.
The Expected value of XX is 1.00.
Given that a box contains 8 cameras and that 4 of them are defective and 2 cameras is selected at random with replacement.
The probability distribution of the hypergeometric is as follows:
[tex]P(x,N,n,M)=\frac{\left(\begin{array}{l}M\\ x\end{array}\right)\left(\begin{array}{l}N-M\\ n-x\end{array}\right)}{\left(\begin{array}{l} N\\ n\end{array}\right)}[/tex]
Where x is the success in the sample of n trails, N represents the total population, n represents the random sample from the total population and M represents the success in the population.
The probability distribution for X is obtained as below:
From the given information, let X be a random variable, that denotes the number of defective cameras following hypergeometric distribution.
Here, M = 4, n=2 and N=8
The probability distribution of X is obtained below:
The probability distribution of X is,
[tex]P(X=x)=\frac{\left(\begin{array}{l}5\\ x\end{array}\right)\left(\begin{array}{l}8-5\\ 2-x\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}[/tex]
The probability distribution of X when X=0 is
[tex]\begin{aligned}P(X=0)&=\frac{\left(\begin{array}{l}4\\ 0\end{array}\right)\left(\begin{array}{l}8-4\\ 2-0\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 0\end{array}\right)\left(\begin{array}{l}4\\ 2\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-0)!0!}\right)\times \left(\frac{4!}{(4-2)!2!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.21\end[/tex]
The probability distribution of X when X=1 is
[tex]\begin{aligned}P(X=1)&=\frac{\left(\begin{array}{l}4\\ 1\end{array}\right)\left(\begin{array}{l}8-4\\ 2-1\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 1\end{array}\right)\left(\begin{array}{l}4\\ 1\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-1)!1!}\right)\times \left(\frac{4!}{(4-1)!1!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.57\end[/tex]
The probability distribution of X when X=2 is
[tex]\begin{aligned}P(X=2)&=\frac{\left(\begin{array}{l}4\\ 2\end{array}\right)\left(\begin{array}{l}8-4\\ 2-2\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left(\begin{array}{l}4\\ 2\end{array}\right)\left(\begin{array}{l}4\\ 0\end{array}\right)}{\left(\begin{array}{l} 8\\ 2\end{array}\right)}\\ &=\frac{\left[\left(\frac{4!}{(4-2)!2!}\right)\times \left(\frac{4!}{(4-0)!0!}\right)\right]}{\left(\frac{8!}{(8-2)!2!}\right)}\\ &=0.21\end[/tex]
Use E(X)=∑xP(x) to find the expected values of a random variable X.
The expected values of a random variable X is obtained as shown below:
The expected value of X is,
E(X)=∑xP(x-X)
E(X)=[(0×0.21)+(1×0.57)+(2×0.21)]
E(X)=[0+0.57+0.42]
E(X)=0.99≈1
Hence, the binomial probability distribution of XX when X=0 is 0.21, when X=1 is 0.57 and when X=2 is 0.21 and the expected value of XX is 1.00.
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AC and BD bisect eachother prove AB || CD and BC ll AD
1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)
4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)
9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)
10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
A function g(x) has x-intercepts at (startfraction 1 over 2 endfraction, 0) and (6, 0). which could be g(x)?
If function has points (1/2,0) and (6,0) then [tex]g(x)=2x^{2} -13x+6\\[/tex]
Given x-intercepts at (1/2,0)(6,0) and we have to find the function g(x)
If the x-intercepts lie at (1/2,0)(6,0) then the function has roots of 6 and 1/2. Function is a relationship between variables having value of y for each value of x. Value of x is domain and value of y is known as codomain.
If we insert x=6 or x=1/2 into the equation of g(x) we will obtain 0 as under:
g(6)=0
In order to get 0 the equation will be x-6.
In order to get 0 for root the equation will be x-1/2.
but x-1/2 does not appear in any of these but its multiples can be there :
[tex]2(x-1/2)=2x-1[/tex]
Therefore the function will be as under:
[tex]g(x)=(x-6)(2x-1)[/tex]
[tex]g(x)=2x^{2} -x-12x+6[/tex]
[tex]g(x)=2x^{2} -13x+6[/tex]
Hence the function g(x) is [tex]g(x)=2x^{2} -13x+6[/tex].
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I dnt really understand WILL GIVE BRAINLIEST THOUGH
Answer: (1, -5)
x = 1
y = -5
*Hope this helps, enjoy the rest of your day! ♥️*
Answer: (1, -5)
Step-by-step explanation:
I got you...
In solving system of equations there are three ways..
lets use addition
First we need to cancel out one of the variables
Lets cancel out the y
In order to do this lets multiply the top equation by -2 to get 2y and 4y to cancel out.
(-2)(-9x+2y) = -19(-2)
18x - 4y = 38
Now our system looks like this:
18x - 4y = 38
5x + 4y = -15
lets add these together
18x - 4y = 38
5x + 4y = -15 +
= 23x = 23
x = 1
We know x = 1, so substitude 1 for x in one of the equations
5(1) + 4y = -15
5 + 4y = -15
4y = -20
y = -5
This is the y value
Our final answer is (1, -5)
As an ordered pair
Jen and marcus got 15 miles up river before they ran out of gas they floated 9 miles back down river before they reached the shore how far did they get
Answer:
they reached the shore they get 135 miles
Line l has slope −4/5, and contains points (a,−6),(−8,a). Determine the value of a. SHOW YOUR WORK
Answer:
a = 2
Step-by-step explanation:
[tex] \frac{a - ( - 6)}{ - 8 - a} = - \frac{4}{5} [/tex]
[tex] \frac{a + 6}{a + 8} = \frac{4}{5} [/tex]
[tex]4(a + 8) = 5(a + 6)[/tex]
[tex]4a + 32 = 5a + 30[/tex]
[tex]a = 2[/tex]
For how many (not necessarily positive) integer values of n is the value 4000x(0.4)^n an integer?
I solved this, nevermind!
The number of integer values of n for which the value 4000 × (0.4)ⁿ is an integer is; 9
How to find the integer values in algebra?We are given the expression;
4000 × (0.4)ⁿ
This can also be expressed as;
4000 × (²/₅)ⁿ which can further be expressed in exponent form as;
(2⁵ × 5³) × (²/₅)ⁿ = 2⁽⁵ ⁺ ⁿ⁾ × 5⁽³ ⁻ ⁿ⁾
Since this expression is an integer, we need:
1) 5 + n ≥ 0 for which n ≥ -5
2) 3 - n ≥ 0 for which n ≤ 3
Taking the intersection gives;
-5 ≤ n ≤ 3
Thus;
Number of Integer Values = 3 - (-5) + 1 = 9
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find the perimeter of each of the rectangles whose sides are given as follows a. 5.5cm and 4.8 cm
Answer:
here is what I came up with 26.4
What is the volume of the composite figure? 6 cm 6 cm 18 cm 6 cm 6 cm 10 cm 8 cm V = [?]cm³ 6 cm What is the volume of the composite figure ? 6 cm 6 cm 18 cm 6 cm 6 cm 10 cm 8 cm V = [ ? ] cm
Answer:
2304 cm³
Step-by-step explanation:
To find the volume of a composite figure, it is easiest to break it down into smaller, more recognizable shapes.
here, we can break our shape into two sections: the green section and the blue section
then, we will add the volumes of these shapes together
green section's volume:
note: you could also calculate this as four separate cubes
to find the volume of a rectangle, we need to multiply
length × width × height
here, our length is 12 (6 + 6); our height is 12 (6 + 6); and our width is 6
let's multiply these together: (12)(12)(6) = 864
so, the volume of the green section is 864 cm³
now, let's work with the blue section:
once again, the volume for a rectangle is length × width × height
here, our length is 18, our height is 10, and our width is 8
let's multiply these together: (18)(10)(8) = 1440
so, the volume of the blue section is 1440cm³
now, we can add our sections together:
1440 + 864 = 2304
meaning that the volume of the composite figure is 2304 cm³
hope this helps!! have a lovely day :)
Patrons (P) Revenue (R)
32
480
500
550
750
33
40
60
81
1,215
Find a linear model for the data.
The linear model for the data is expressed as: R = 20p - 160.
How to Write a Linear Model?Using two pairs of values from the table values, say, (32, 480) and (33, 500), find the unit rate (m).
Unit rate (m) = (500 - 480)/(33 - 32) = 20/1
Unit rate (m) = 20.
Substitute (p, R) = (32, 480) and m = 20 into R = mp + b to find b
480 = 20(32) + b
480 = 640 + b
480 - 640 = b
b = -160
To write the linear model, substitute m = 20 and b = -160 into R = mp + b:
R = 20p - 160
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please help me im in a rush 25 points
Answer:
74 yards squared
Step-by-step explanation:
Divide the shape up into 2 3x5 rectangles and one 11x4 rectangle
2(3x5)+11x4=30+44=74
74 yards squared
Are these two angles corresponding?
Answer:
Yes they are
Step-by-step explanation:
Because AE and FD both make a 50 degree angle with AC they are parallel which means that the two angles are corresponding.
Select the correct answer. Find the inverse of the given function. f(x) = (x+3)^3-1
The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
How to determine the inverse function?The function is given as:
f(x) = (x + 3)^3 - 1
Rewrite as:
y = (x + 3)^3 - 1
Swap x and y
x = (y + 3)^3 - 1
Add 1 to both sides
(y + 3)^3 = x + 1
Take the cube root of both sides
[tex]y + 3 = \sqrt[3]{x + 1}[/tex]
Subtract 3 from both sides
[tex]y = \sqrt[3]{x + 1} - 3[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground? don’t play if you’re not to continue.
Considering the number of legs of each animal, it is found that there are 56 legs on the ground.
How many legs does each animal have?Dogs have 4 legs.Horses have 9 legs.Giraffes have 4 legs.Ducks have 2 legs.Chickens have 2 legs.Hence the number of legs on the ground is given by:
N = 2 x 4 + 4 x 9 + 1 x 4 + 1 x 2 + 3 x 2 = 56.
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Which is larger? a or -a
Answer:
a. a is bigger than -a
b. a is equal to -a
c. a is less than -a
Step-by-step explanation:
Let's say a = 2
If a > 0, 2 > -2
If a = 0, 0 = -0; -0 and 0 are the same
Let's say a = -1
If a < 0, -1 ? -(-1)
-1 < 1
Prism A is similar to Prism B. The volume of Prism A is 4320 cm³.
What is the volume of Prism B?
34,560 cm³
2160 cm³
1080 cm³
540 cm³
Rectangular prism A has a right angle in one corner of its base, and one side of the base is twelve centimeters. Rectangular prism B has a right angle in one corner of its base, and the same one side of the base is six centimeters.
Answer:
D
Step-by-step explanation:
the question is in the attached picture
Answer: [tex]\frac{1}{3} \sin x^{3}+C[/tex]
Step-by-step explanation:
Let [tex]u=x^3[/tex]. Then, [tex]3x^2 dx = du \longrightarrow x^2 dx =\frac{1}{3}du[/tex]
So, we can rewrite the original integral as
[tex]\frac{1}{3} \int \cos u \text{ } du=\frac{1}{3} \sin u+C=\frac{1}{3} \sin x^{3}+C[/tex]
Please help me with this linear inequalities as graphs question!
I'd really appreciate if you added workings out and explained it a bit, as I'm terribly stuck.
The system of linear inequalities which satisfy the region R in the graph above are:
y ≤ 2x + 3y ≥ -x + 4y ≤ x + 4How to find the inequalities?Mathematically, the general equation of a straight line is given by y = mx + b.
In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which these straight lines passes through.
For the left line, we have:
y-intercept = 3.
x-intercept = -3/2.
Points (x, y) = (0, 3) and (-3/2, 0).
Thus, the inequality is given by:
(x/-3/2) + y/3 ≤ 1.
-2x + y ≤ 3
y ≤ 2x + 3
For the right line, we have:
y-intercept = 4.
x-intercept = 4.
Points (x, y) = (0, 4) and (4, 0).
Thus, the inequality is given by y ≥ -x + 4
For the lower line, we have:
y-intercept = 0.
x-intercept = 4.
Points (x, y) = (4, 0)
Thus, the inequality is given by y ≤ x + 4
In conclusion, the system of linear inequalities which satisfy the region R in the graph above are:
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Omar is playing a computer game. He starts with 0 points wins 8 points loses 6 points 4 times and the wins 2 points. Which integer represents Omar’s score
The integer that represents Omar's score is -14.
What is the integer represents Omar’s score?Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.
When Omar wins, the points are added and when he losses, the points are subtracted.
0 + 8 - (6 x 4) + 2
0 + 8 - 24 + 2 = -14
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There are 5 trees with 6 birds in each tree. 4 birds fly away. How many birds are left?
Angela has 108 pieces of candy. If she gives each person 4 pieces, how many people can she give candy to?
If diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? round the answer to the nearest tenth of a foot. 10.3 ft 17.6 ft 30.2 ft 97.2 ft
Answer:
17.6 ft
Step-by-step explanation:
tan 37 = 130/x
x = 130/tan 37 = 130/0.7536 = 172.5 feet
tan 40 = 130/y
y = 130/tan 40 = 130/0.8391 = 154.9
172.5 - 154.9 = 17.6 ft
Answer:
17.6 Ft
Step-by-step explanation:
Geometry B E2020!! :3
One fifth of r is 15 how would I write that in an equation
Answe1/5 of r = 15
Step-by-step explanation:
1/5 r=
Write an algebraic equation to match this graph.
Using translation concepts, the algebraic equation that matches the graph is given by:
y = |x - 1| - 1
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function y = |x| is:
Shifted one unit right, hence x -> x - 1.Shifted one unit down, hence y -> y - 1.Thus the algebraic equation that matches the graph is given by:
y = |x - 1| - 1
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PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE BRAINL
The average rate of change from x=1 to x= 4 is -0.7
How to solve for the rate of changeWe have f(1) to be 3
while we have f(4) as 1
The average rate of change can be solved as
f(4) - (f(1) / 4 - 1
This is solved as
1 - 3 / 4 - 1
= -2 / 3
= -0.7
Hence the average rate of change for the graph that we have above is -0.7
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