We can find the measure of angles RQS and TQS by applying the theorem below:
The sum of angles on a straight line is 180 degrees
Given:
\(\begin{gathered} m\angle RQS=(20x+4)^0 \\ m\angle TQS=(15x+1)^0 \end{gathered}\)Applying the theorem, we have:
\((20x+4)^0+(15x+1)^0=180^0\text{ (angles on a straight line)}\)Simplifying and solving for x:
\(\begin{gathered} 20x\text{ + 4 + 15x + 1 =180} \\ \text{Collect like terms} \\ 20x\text{ + 15x + 5 =180} \\ 35x\text{ = 180-5} \\ 35x\text{ = 175} \\ Divide\text{ both sides by 35} \\ \frac{35x}{35}\text{ = }\frac{175}{35} \\ x\text{ = 5} \end{gathered}\)When we substitute the value of x , we can find the required angles.
Hence:
\(\begin{gathered} m\angle RQS=(20x+4)^0 \\ =\text{ 20}\times5\text{ + 4} \\ =\text{ 100 + 4} \\ =104^0 \end{gathered}\)Answer: measure of angle RQS = 104 degrees
\(\begin{gathered} m\angle TQS=(15x+1)^0 \\ =\text{ 15 }\times\text{ 5 + 1} \\ =\text{ 75 + 1} \\ =76^0 \end{gathered}\)Answer: measure of angle TQS = 76 degrees
determine the product
800.5 x (2 x 56)
Answer: 89656
this is the answer your short
halp me plss halp me
Answer:
14m
Step-by-step explanation:
To find the diagonal length of the triangle, your formula will be a² + b² = c²
the side length is a
and the base length is b
6 + 8 = 14
You have been halped
7,600 dollars is placed in a savings account with an annual interest rate of 6%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answers:
M=7,600(1+0.06)(1+0.06)
M=7,600(1-0.06)^7
M=7,600(1+0.06)^7
M=7,600(0.06)^7
Step-by-step explanation:
The equation that represents how much will be in the account after 7 years is:
M = 7,600(1+0.06)^7
Here's the explanation:
The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.
In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.
Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.
can someone help me solve this problem (graphing/geometry)
Answer:
24
Step-by-step explanation:
i quessed
g(a) = 2a - 1
hla) = 3a – 3
Find (g. h)(-4)
Step-by-step explanation:
(g. h)(-4) = g(4).h(4)
= [2(4)-1].[3(4)-1]
=7×11
=77
Scientists have increased their ability to make observations beyond their own senses through the invention of specialized equipment such as xray telescopes. which best explains how such technology has affected society?
The human understanding of the cosmos beyond Earth has grown after inventing specialized equipment such as x-ray telescopes.
What is x-ray telescopes?X-ray telescope, a device made to find and focus X-rays from sources beyond the atmosphere of Earth.
Some key features regarding the x-ray telescope are-
X-ray telescopes have to be launched into orbit outside of the atmosphere or propelled to great heights by rockets and balloons due to atmospheric absorption. While telescopes carried aloft using rockets or satellites serve to detect softer radiation, balloon-borne telescopes may catch the more piercing (harder) X-rays.That sort of telescope must have a completely different design from a typical optical telescope. Since X-ray photons are so energetic, a typical reflector's mirror wouldn't be able to stop them from passing through. If X-rays are to be collected, they must bounce off a reflector at an extremely low angle.To know more about x-ray telescope, here
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Grant paddled a canoe
34 mile in 12 hour. How fast did Grant paddle in miles per hour? (2pts) (Hint: Insert a table to help solve)
Answer:
2.83 miles per hour
Step-by-step explanation:
Just divide the amount of miles by how many hours it took her too paddle that far.
Use the cosine of a sum and cosine of a difference identities to find cos(s+t) and cos(s−t). sins= 13
12
and sint=− 5
3
,s in quadrant I and t in quadrant III cos(s+t)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cos(s−t)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
The cosine of a sum and cosine :cos(s+t) = cos(s−t) = -5/4.
To find cos(s+t) and cos(s−t), we can use the cosine of a sum and cosine of a difference identities.
Given:
sin(s) = 13/12 (s in quadrant I)
sin(t) = -5/3 (t in quadrant III)
First, let's find cos(s) and cos(t) using the:
cos(s) = √(1 - sin^2(s)) = √(1 - (13/12)^2) = √(1 - 169/144) = √(144/144 - 169/144) = √((-25)/144) = -5/12
cos(t) = √(1 - sin^2(t)) = √(1 - (-5/3)^2) = √(1 - 25/9) = √(9/9 - 25/9) = √((-16)/9) = -4/3
Using the cosine of a sum identity: cos(s+t) = cos(s)cos(t) - sin(s)sin(t)
cos(s+t) = (-5/12)(-4/3) - (13/12)(-5/3) = 20/36 - 65/36 = -45/36 = -5/4
Using the cosine of a difference identity: cos(s−t) = cos(s)cos(t) + sin(s)sin(t)
cos(s−t) = (-5/12)(-4/3) + (13/12)(-5/3) = 20/36 - 65/36 = -45/36 = -5/4
Therefore, cos(s+t) = cos(s−t) = -5/4.
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Least common denominator of 11/12 and 3/4
Answer:
12
Step-by-step explanation:
LCD = 12
Hope this helps!
PLEASE HELP ME I BEG OF YOU!!!!!
SHOW ALL WORK!
Answer:
243π
Step-by-step explanation:
Area of the entire circle = πr² = π18² = 324π
Area of sector = (90/360)π(18)² = 81π
Shaded area = 324π - 81π = 243π
JEN PURCHASED THE ITEM SHOWN IN THE TABLE IN THE CITY IN THE SALES TAX RATE IS 7.15 IN ANOTHER CITY THE SALES TAX RATE IS 6.35 HOW MUCH MORE IS SHE SPENDING IF SHE PURCHASED THE ITEM==EN IN THE CITY WHERE SHE LIVES
Answer:
First, calculate the amount of sales tax by multiply the percent tax times the total cost:
0.07×600 =42
Next, add the amount of tax to the price of the computer:
600+42=642
$0.45792 more is she spending if she purchases the items in the city where she lives.
Given that, Jen purchased the items shown on the table. In the city she lives in, the sales tax rate is 7.15%. In another city, the sales tax rate is 6.35%.
We need to find out how much more is she spending if she purchases the items in the city where she lives.
What is the sales tax?A sales tax is a consumption tax imposed by the government on the sale of goods and services.
Now, the cost of the goods she purchased=11.99+35.50+6.75+3.00
=$57.24
The sales tax rate is 7.15%.
So, the sales tax=7.15% of 57.24
=$4.09266
The sales tax rate is 6.35%.
So, the sales tax=6.35% of 57.24
=$3.63474
Now, 4.09266-3.63474=$0.45792
Therefore, $0.45792 more is she spending if she purchases the items in the city where she lives.
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suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 60 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? people (b) how many would you expect to be taller than 167 cm?
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.
μ = 170
σ = 5
n = 60
(a) The probability would you expect to be between 165 and 175 cm tall;
P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )
= P( -1 < z < 1 )
= P( z < 1) - P( z < -1 )
= 0.8413 - 0.1587
= 0.6826
Expected number of people between 165 and 175 = n * p
= 60 * 0.6826
= 40.956
≅ 41
(b) The probability would you expect to be taller than 167 cm;
P( x > 167 ) = P( z > (167 - 170)/5 )
= P( z > -0.6 )
= 0.7257
Expected number of people taller than 168 = n * p
= 60 * 0.7257
= 43.542
≅ 39
Hence,
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
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what is the equation of the mjddle for the function f(x)?
f(x)=3cos(x)-2.5
please give brainliest
Answer:
To shift the graph of the function f(x) = cos(x) downward by 2.5 units, you can subtract 2.5 from the function. The equation of the middle for the shifted function would be:
f(x) = cos(x) - 2.5
Answer:
y=-2.5
Step-by-step explanation:
f(x) =0 -2.5
y=-2.5
Hope this helped buddy
peace ️
x^2+y^2-28x-10y+220=0
This is the equation of a circle is (x - 14)² + (y - 5)² = 1 with center at (14, 5) and radius 1.
Starting with the x terms:
x² - 28x
= x² - 28x + 196 - 196
= (x - 14)² - 196
And now for the y terms:
y² - 10y
= y² - 10y + 25 - 25
= (y - 5)² - 25
Substituting these into the original equation gives:
(x - 14)² - 196 + (y - 5)² - 25 + 220 = 0
Simplifying gives:
(x - 14)² + (y - 5)² = 1
This is the equation of a circle with center at (14, 5) and radius 1.
To graph this, plot the point (14, 5) and draw a circle with radius 1 around it.
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A large manufacturing company is being sued for false advertisement because 15% of the batteries in its shipping boxes are defective, but the company claims that only 5% are defective. You plan to use hypothesis testing to determine whether there is significant evidence that the company is falsely advertising.
Part A: State the null and alternate hypotheses for the significance test. (2 points)
Part B: In the context of the problem, what would a Type I error be? A Type II error? (2 points)
Part C: If the hypothesis is tested at a 5% level of significance instead of 1%, how will this affect the power of the test? (3 points)
Part D: If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, how will this affect the power of the test? (3 points)
The required solution for the hypothesis testing is shown.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
Part A:
The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.
The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.
H0: p ≤ 0.05
Ha: p > 0.05
where p represents the proportion of defective batteries.
Part B:
A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.
A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.
Part C:
If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.
Part D:
If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.
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what is the distributive property of 24+28
Answer:
4(6+7)
Explanation:
24+28
(4×6)+(4×7)
4(6+7)
Find the Error A student states that the exterior angle of a triangle can never be a right angle. Find the mistake and correct it.
Answer:
There is no photo here so sorry.
Step-by-step explanation:
A student states that the exterior angle of a triangle can never be a right angle. The statement is incorrect.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
A student states that the exterior angle of a triangle can never be a right angle.
The given statement is incorrect because, in the right-angle triangle, the interior and exterior angles are equal that is right angle.
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Help me help me help me
Answer:
the answer is ____
Step-by-step explanation:
first study more
then clean that computer
and then dont ask on here okau
The volume of a pyramid with base area B and height h is
1
3
Bh. Brian designed a trophy shaped like a pyramid for the math club's most improved member. The trophy is 10 inches tall and has a base area of 6.6 square inches.
What is the volume of the trophy?
Write your answer as a whole number or decimal.
The volume of the trophy that has a pyramid shape is: 22 cubic inches.
How to Find the Volume of a Pyramid?The volume of a pyramid can be calculated by multiplying the area of the base of the pyramid together with the height of the pyramid, then divide by 3.
Volume of a pyramid is given as: V = 1/3(B)(h), where B is the base area of the pyramid and h is the height of the pyramid.
The given parameters of the pyramid-shaped trophy are:
Base area of the pyramid (B) = 6.6 square inches
Height of the pyramid (h) = 10 inches
Substitute B = 6.6 and h = 10 into V = 1/3(B)(h):
Volume of the pyramid-shaped trophy = 1/3(B)(h) = 1/3(6.6)(10)
Volume of the pyramid-shaped trophy = 1/3(B)(h) = 1/3(6.6)(10)
Volume of the pyramid-shaped trophy = (1 × 6.6 × 10)/3
Volume of the pyramid-shaped trophy = (66)/3
Volume of the pyramid-shaped trophy = 22 cubic inches.
In summary, the volume of the trophy that has a pyramid shape is: 22 cubic inches.
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HURRY PLEASE!
Which function matches the following description?
"when finding the difference of the input and six, you will get the output"
A. x=y-6
B.y = 6 x
C.y=x-6
D. x = 6-y
Answer:
C. y=x-6
Step-by-step explanation:
x is input
y is output
difference is subtraction
Answer:
C.y=x-6
Step-by-step explanation:
x is input
y is output
output = input - 6
y = x - 6
Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9%
compounded annually. How much will be available for Peter’s child education?
Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore, the amount available for Peter's child education will be $147,330.55.
Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,
The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.
In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r
where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.
Using the above formula; the future value of Michael's savings is:
FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55
Therefore, the amount available for Peter's child education will be $147,330.55.
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Im so confused on what do to here
Ans. (a)
SQ and RQ
Ans. (b)
∠RQT
∠TQR
Ans. (c)
Q
i need help with dis oki
Answer:
15 mph
Step-by-step explanation:
You need to find how much each side of the table is changing each time and change that into a fraction. In this example, the change in time is .5 hours. Repeat with the other side to get 12.5 miles. Next you change it into a fraction with the distance over the time to get 12.5/.5. Type this into the calculator to get the answer which is 15 mph.
Alice has been in a defined-contribution pension scheme since she was 35 and will retire in one year’s time at age 66. Her salary is currently £55,000. Throughout her enrolment in the scheme, she has paid in 8% of salary, and this has been topped up by employer contributions and tax relief worth 4% of salary. She will also qualify for a state pension of £9,000 per year.
If Alice uses her whole pension fund to buy an index-linked annuity, how much income will she receive in her first year of retirement?
To calculate the income Alice will receive in her first year of retirement, we need to consider her pension fund, the state pension, and the annuity rates.
Given: Alice's salary: £55,000
Her contributions to the pension scheme: 8% of salary
Employer contributions and tax relief: 4% of salary
Retirement age: 66
State pension: £9,000 per year
First, let's calculate Alice's pension fund. She has been in the scheme from age 35 to 66, which is a total of 31 years. During this period, she has made contributions of 8% of her salary, topped up by 4% from the employer and tax relief. So, her annual contributions are (8% + 4%) of £55,000 = £5,500.
Her total pension fund would be £5,500 x 31 = £170,500.
Next, let's consider the annuity rates. Annuity rates determine the income that can be purchased with the pension fund. The rates vary based on factors such as age, gender, and prevailing market conditions.
Using the annuity rates, Alice can calculate the income she will receive from her pension fund. Let's assume the annuity rate is 5% per year. So, the income from her pension fund would be £170,500 x 5% = £8,525.
Finally, we add the state pension to calculate Alice's total income in her first year of retirement:
Total income = Pension fund income + State pension
Total income = £8,525 + £9,000 = £17,525.
Therefore, Alice will receive £17,525 as her income in the first year of retirement.
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You roll a ten-sided number polyhedron that has the numbers 1 through 10 on its faces. Each face has a different number. You observe the number that ends up on top. Let A be the event “the number is less than 6” and B be the event “the number is odd”.
A. Find P(A), P(B), and P(A and B).
B. Find P(A)+P(B)−P(A and B).
C. Find P(A or B).
Answer:
I am not good at those but I am pretty sure its between a or b
1) How is unit rate related to slope or rise over run?
Can there be a multiple linear regression equation between one dependent and one independent variable?
a) Yes
b) No
No, there cannot be a multiple linear regression equation between one dependent and one independent variable.
Multiple linear regression involves the use of two or more independent variables to predict a single dependent variable. In the case of one dependent and one independent variable, simple linear regression is used instead. Simple linear regression models the relationship between the two variables with a straight line equation, while multiple linear regression models the relationship with a multi-dimensional plane.
Multiple linear regression is a statistical technique used to model the relationship between a dependent variable and two or more independent variables. The goal of multiple linear regression is to create an equation that can predict the value of the dependent variable based on the values of the independent variables. In contrast, simple linear regression involves modeling the relationship between one dependent variable and one independent variable. The equation for a simple linear regression model is a straight line, which can be used to predict the value of the dependent variable based on the value of the independent variable. Therefore, there cannot be a multiple linear regression equation between one dependent and one independent variable, as multiple linear regression requires at least two independent variables.
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Okay i have to do a whole test and i need help!!
The picture is up there!
Answer:
a is triangular prism :)
Answer:
Before you take a proctored exam, make sure have approved ID verification photos ... Photo verification may take up to 5 days to process, so please make sure to ... approval above, you would also need to complete onboarding exam 5 days
Step-by-step explanation:
Find the y-intercept of each line defined below and compare their values.
Equation of Line A:
y = -3x+3
Graph of Line B:
The y-intercept of Line A is
Therefore the y-intercept of Line A is
and the y-intercept of Line B is
the y-intercept of
The y-intercept of line A is 3, and the y-intercept of line B is 4.
How to find the y-intercepts of the lines?For any function y = f(x), we define the y-intercept as the value that y takes when x = 0.
For the first linear equation we have:
y = -3x + 3
Evaluating in x = 0 we will get:
y = -3*0 + 3
y = 3
The y-intercept is 3.
For the other function we can see that the line intercepts the y-axis at y = 4, so that is the y-intercept.
Then the y-intercept of Line A is 3 and the y-intercept of Line B is the y-intercept of 4.
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the distribution of cholesterol levels in teenage boys is approximately normal with mean of 170 and standard deviation 25 (source: u.s. national center for health statistics). levels above 200 warrant attention. find the probability that a teenage boy has a cholesterol level greater than 200. group of answer choices
The probability that a teenage boy has a cholesterol level greater than 200 is 0.11507.
Let the distribution of teenage boys' cholesterol levels be x
According to the question,
X follows a Normal distribution with
mean = 170
Standard deviation = 25
Hence, the variance = 25² = 625.
Hence X ~ N(170,25)
Now we need to find P(X>200)
= 1 - P(X<200)
Now to find this we need to convert the problem to a standard normal distribution
for this, we use the formula
P(X<x) = P(Z<x-mean/sd)
Therefore,
P(X<200)
= P(Z<(200 - 170)/25)
= P(Z<30/25)
= P(Z<1.2)
According to Z table,
P(Z<1.2)
= 0.88493
Hence, P(X>200)
= 1 - 0.88493
= 0.11507
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