9514 1404 393
Answer:
m∠QPR = 94°
Step-by-step explanation:
Given:
m∠QPS = 180°
m∠QPR = 7x -4°
m∠RPS = 9x -40°
Find:
m∠QPR
Solution:
m∠QPR + m∠QPR = 180°
(7x -4°) +(9x -40°) = 180°
16x = 224° . . . . . . . . . . . . . add 44°
x = 14° . . . . . . . . . . . . . divide by 16
m∠QPR = 7x -4° = 7(14°) -4°
m∠QPR = 94°
A carpenter is constructing staircase in a house. The distance from the floor to the basement is 10.8 feet. The staircase will be 16.6 feet long. What angle do the stairs make with the basement floor?
Answer:
[tex]\theta = 40.59^\circ[/tex]
Step-by-step explanation:
Given
The question is illustrated with the attached image
Required
Find [tex]\theta[/tex]
To do this, we use sine formula
i.e.
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(\theta) = \frac{10.8}{16.6}[/tex]
[tex]\sin(\theta) = 0.6506[/tex]
Take arc sin
[tex]\theta = \sin^{-1}(0.6506)[/tex]
[tex]\theta = 40.59^\circ[/tex]
Jeff's bowling scores are approximately normally distributed with mean 100 and standard deviation 21, while Pam's scores are normally distributed with mean 155 and standard deviation 22. If Jeff and Pam each bowl one game, then assuming that their scores are independent random variables, approximate the probability that
a. the total of their scores is above 260.
b. Jeffs score is higher.
Answer:
a. 0.4364 = 43.64% probability that the total of their scores is above 260.
b. 0.0351 = 3.51% probability that Jeff's score is higher.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Sum/Subtraction between normal variables:
When two normal variables are added/subtracted, the mean is the sum/subtraction of the means, while the standard deviation is the square root of the sum of the variances.
a. the total of their scores is above 260.
Mean is the sum of the means, so:
[tex]\mu = 100 + 155 = 255[/tex]
Standard deviation is the square root of the sum of the variances. So
[tex]\sigma = \sqrt{21^2+22^2} = 30.4[/tex]
The probability is 1 subtracted by the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 255}{30.4}[/tex]
[tex]Z = 0.16[/tex]
[tex]Z = 0.16[/tex] has a p-value of 0.5636
1 - 0.5636 = 0.4364
0.4364 = 43.64% probability that the total of their scores is above 260.
b. Jeff's score is higher.
Jeff's mean is of 100, while Pam's is of 155. The probability of Jeff's score being higher is the probability that the subtraction is above 0. The mean is:
[tex]\mu = 100 - 155 = -55[/tex]
The probability is 1 subtracted by the p-value of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-55)}{30.4}[/tex]
[tex]Z = 1.81[/tex]
[tex]Z = 1.81[/tex] has a p-value of 0.9649.
1 - 0.9649 = 0.0351
0.0351 = 3.51% probability that Jeff's score is higher.
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. The net weights actually vary slightly from bag to bag and are normally distributed with mean μ. A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised.
For this, the representative randomly selects 16 bags of this brand and determines the net weight of each. He finds the sample mean to be 13.82 and the sample standard deviation to be 0.24.
Use these data to perform an appropriate test of hypothesis at 5% significance level.
Answer:
The p-value of the test is of 0.0045 < 0.05, which means that there is enough evidence to reject the null hypothesis and accept the alternate hypothesis that the mean net weight is less than advertised.
Step-by-step explanation:
Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised.
At the null hypothesis, we test that the mean is of 14, that is:
[tex]H_0: \mu = 14[/tex]
At the alternate hypothesis, we test tha tthe mean is less than advertised, that is, less than 14. So:
[tex]H_a: \mu < 14[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
14 is tested at the null hypothesis:
This means that [tex]\mu = 14[/tex]
For this, the representative randomly selects 16 bags of this brand and determines the net weight of each. He finds the sample mean to be 13.82 and the sample standard deviation to be 0.24.
This means that [tex]n = 16, X = 13.82, s = 0.24[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.82 - 14}{\frac{0.24}{\sqrt{16}}}[/tex]
[tex]t = -3[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean below 13.82, which is the p-value of t = -3, using a left-tailed test with 16 - 1 = 15 degrees of freedom.
With the help of a calculator, the p-value is of 0.0045.
The p-value of the test is of 0.0045 < 0.05, which means that there is enough evidence to reject the null hypothesis and accept the alternate hypothesis that the mean net weight is less than advertised.
A rock climber is planning to climb a mountain cliff over two days. The climb begins at an altitude of 6,400 feet above sea level. The rock climber figures
he can climb at an average pace of 360 feet per hour. He wants to climb to an altitude higher than 8,020 feet above sea level by the end of the first day of
climbing.
Which inequality and solution describe how many hours the climber must climb on the first day to reach his goal?
A
360h + 6,400 < 8,020, with a solution of h < 4
2
B
360h + 6,400 < 8,020, with a solution of h < 7
71
C
360h + 6,400 > 8,020, with a solution of h > 75
18
D
360h + 6,400 > 8,020, with a solution of h > 4.
2
Answer:
D
Step-by-step explanation:
360h+6,400 >8,020, with a solution is h> 4.
CAN SOMEONE PLEASE HELP ASAP!!
Answer:
42.9
Step-by-step explanation:
There are many ways to answer this one, the most direct way would be to state that tan(65)=a/20
20tan(65)=a
Using the calculator (set in degree mode)
we find that a ~ 42.9
1. These are the first sentences in the short story, "The Gift of the Magi," by O. Henry:
"One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies."
Model the scenario with an equation. Let q be the number of quarters, d be the number of dimes, and n be the number of nickels.
25 q + 10 d + 5 n + 60 = 1.87
0.25 q + 0.10 d + 0.5 n + 0.60 = 187
q + d + n + 60 = 187
25 q + 10 d + 5 n + 60 = 187
2. These are the first sentences in the short story, "The Gift of the Magi," by O. Henry:
"One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies."
A. Simplify the equation that represents the value of the coins. Make it an equation that expresses the value of quarters, dimes, and nickels. Show your work.
B. Is it possible to have exactly 60 pennies in $1.87? Explain.
I will give brainliest if correct.
Answer:
I think the answer to this is: 25q + 10d + 5n + 60 = 87
The story says that you have 1 dollar and 87 cents; 60 cents of which is pennies. So, if you’re using an equation involving quarters, dimes and nickels, the total equation should equal to 87 cents (since that dollar bill could not be broken down to cents).
Step-by-step explanation:
i promise
Of number 4, 6, 8, determine which number is a solution of the inequality 5 + c < 10
answer:
4 is the answer to the question
5. ¿Cuál es el resultado de simplificar a su minima expresión el siguiente
polinomio?:
2
3 3*
xy2 + 2x + 3xy2 + {x?y=5x
Answer:
El polinomio final es:
[tex]=x(\frac{1}{3}y^{2}-3+\frac{2}{3}xy)[/tex]
Step-by-step explanation:
Agrupemos los términos con las mismas variables:
[tex](\frac{2}{3}xy^{2}-\frac{1}{3}xy^{2})+(2x-5x)+\frac{2}{3}x^{2}y=[/tex]
Sumemos estos terminos:
[tex]=\frac{1}{3}xy^{2}-3x+\frac{2}{3}x^{2}y=[/tex]
Podemos ver que los tres terminos tienen x, asi que podemos factorizar x.
Por lo tanto el polinomio final es:
[tex]=x(\frac{1}{3}y^{2}-3+\frac{2}{3}xy)[/tex]
Espero te haya servido.
El resultado de simplificar [tex]\frac{2}{3}xy^2+2x-\frac{1}{3}xy^2+\frac{2}{3}x^2y-5x[/tex] es
[tex](\frac{1}{3}y^2+\frac{2}{3}xy-3)x[/tex]
El polinomio que queremos simplificar es
[tex]\frac{2}{3}xy^2+2x-\frac{1}{3}xy^2+\frac{2}{3}x^2y-5x[/tex]
primero, recopilamos términos similares
[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2+\frac{2}{3}x^2y+2x-5x[/tex]
luego simplificamos los términos similares. Es decir
Para el [tex]xy^2[/tex] términos:
[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2=(\frac{2}{3}-\frac{1}{3})xy^2\\\\=(\frac{1}{3})xy^2=\frac{1}{3}xy^2[/tex]
y para el [tex]x[/tex] términos:
[tex]2x-5x=(2-5)x\\=(-3)x=-3x[/tex]
la [tex]x^2y[/tex] términos ya está simplificado. Así que déjalo así.
Este es el trabajo total:
[tex]\frac{2}{3}xy^2-\frac{1}{3}xy^2+\frac{2}{3}x^2y+2x-5x\\\\=(\frac{2}{3}-\frac{1}{3})xy^2+\frac{2}{3}x^2y+(2-5)x\\\\=(\frac{1}{3})xy^2+\frac{2}{3}x^2y+(-3)x\\\\=\frac{1}{3}xy^2+\frac{2}{3}x^2y-3x[/tex]
Incluso podemos factorizar la respuesta final para obtener
[tex](\frac{1}{3}y^2+\frac{2}{3}xy-3)x[/tex]
Obtenga más información sobre la simplificación aquí: https://brainly.com/question/25014973
How do you write 7.67 x 102 in standard form?
WILL MARK BRAINLIEST IF RIGHT IS GIVEN ‼‼‼
The circular radio signal from transmitter A has three times the radius of the circular signal from transmitter B. How many times greater is the area of the signal from transmitter A than from transmitter B?
Answer:
It is 3 times bigger in diameter and size.
Step-by-step explanation:
Multiply the radio transmission from B, to A
Hope this Helps!
-kiniwih426
Answer:
3 times bigger
Step-by-step explanation:
A scale drawing of a park can be seen below. If 1 inch is equal to 15 feet. What is the actual area of the park
Answer:
Where's the drawing? Can you include it?
Step-by-step explanation:
20. Given circle C with radius r and circle D with radius
s, what is an appropriate first step when proving
circle C is similar to circle D?
O A. Transform circle C with a dilation that has center
Cand scale factors.
B. Transform circle C with a dilation that has center
C and scale factor r.
O C. Transform circle C with the translation that maps
point Conto point D.
OD. Transform circle C with the translation that maps
point onto point C.
Answer:
A. Transform circle C with a dilation that has center C and scale factor s.
Step-by-step explanation:
Given
Circle C
[tex]radius = r[/tex]
Circle D
[tex]radius = s[/tex]
Required
Map C to D
From the question, we can assume that:
[tex]r \ne s[/tex]
This implies that options c and d are false because when an object is translated from one point to another, the size of the object remains unchanged.
To map C onto D,
1) C has to be dilated from its own center C
2) The scale of dilation will be equal to the radius of D (i.e. s)
Hence, (A) is correct
Answer:
It's C
Transform circle C with the translation that maps point Conto point D.
9. A shipping box is shaped like a rectangular prism. The dimensions of the box are in inches, as shown below.
(w+5) inches
(w+4) inches."
(2w) inches
Which expression describes the volume, in cubic inches, of the box?
A. 2w3 + 9w + 20
B. 243 + 182 + 402
C. 2u2 + 18w + 40
D. 2w2 + 4w+5
Given:
The dimensions of the box are (w+5) inches, (w+4) inches, (2w) inches.
To find:
The expression that describes the volume of the box.
Solution:
We know that the volume of a rectangular prism is:
[tex]V=length\times breadth \times height[/tex]
Substituting the given values, we get
[tex]V=(w+5)\times (w+4) \times 2w[/tex]
[tex]V=(w^2+5w+4w+20)2w[/tex]
[tex]V=(w^2+9w+20)2w[/tex]
Using distribution property, we get
[tex]V=(w^2)2w+(9w)2w+(20)2w[/tex]
[tex]V=2w^3+18w^2+40w[/tex]
Therefore, the volume of the box is [tex]2w^3+18w^2+40w[/tex] cubic inches.
Note: All the options are incorrect.
PLssssssssssssssssssssssssssssssssss help.
Answer:
C
Step-by-step explanation:
whats equivalent to 3(7 + x).
Answer: 21+3x
Step-by-step explanation: simply distribute the three into the parentheses
Hope this helps
Answer:
21+3x
Step-by-step explanation:
you multiply 3 by 7 and then you sum it with 3 multiplied by x hope i helped
find the volume of the prism
Answer:
The volume is: [tex]135m^3[/tex]
Step-by-step explanation:
Given
[tex]h = 5m[/tex] ---- height
[tex]l=9m[/tex] -- length
[tex]w = 6m[/tex] --- width
Required
Determine the volume (V)
The volume of a triangular prism is:
[tex]V = 0.5lwh[/tex]
So, we have:
[tex]V = 0.5 * 5m * 9m * 6m[/tex]
[tex]V = 135m^3[/tex]
15. If 8x + 6x + 5x + 3x = 440, then
2x + 5.8=
Answer:
2x + 5.8= 45.8
Step-by-step explanation:
8x + 6x + 5x + 3x = 440
combine like terms:
22x = 440
divide both sides of the equation by 22:
x = 20
2x + 5.8= 40 + 5.8 = 45.8
Create a proportion for each set of similar triangles. Then solve the missing parts
Help please!
bot answers will be reported
determine which graphic represents a function
Budgeting and you MI-Economics assignment question. Now, summarize what you have learned. Write a paragraph that explains the most important principles to keep in mind when creating a budget. Describe at least three important principles in your answer.
Answer:
It all starts by setting clear goals. You need to know what you want to accomplish in the short term and the long term. Then, you can examine your goals to find your needs and wants. You can accomplish these needs and wants by categorizing your expenses into fixed and variable categories. By keeping all of these principles in mind, you will be able to balance your budget. This will allow you to save money while also spending enough to meet your goals.
Step-by-step explanation:
Answer:
Sample Response: It all starts by setting clear goals. You need to know what you want to accomplish in the short term and the long term. Then, you can examine your goals to find your needs and wants. You can accomplish these needs and wants by categorizing your expenses into fixed and variable categories. By keeping all of these principles in mind, you will be able to balance your budget. This will allow you to save money while also spending enough to meet your goals.
Step-by-step explanation:
edg 2022
Determine the restricted domain of the graph shown.
Answer:
The answer is all real numbers is smaller than 2.
Step-by-step explanation:
PLS HURRY. WILL MARK BRAINLEST!!!! JWKSNWN PLEASE I NEED IT!!
Answer:
B
Step-by-step explanation:
Mark me brainliest PLZ
Is the answer A, B, C, or D?
Answer:
A
Step-by-step explanation:
2 3/8=19/8=2.375
22. What is the mean of these
numbers?
2, 5, 4, 9, 5
Answer:
5
Step-by-step explanation:
Answer:
the mean is 5
Step-by-step explanation:
help me please?? solve using proportion
9514 1404 393
Answer:
2 1/2 cups
Step-by-step explanation:
A proportion says the ratio of one thing to another is the same for different amounts. Here, we want cups, so we can use the proportion ...
cups/people = 2/12 = x/15 . . . . . where x is the number we want to find
Multiplying by 15 gives ...
x = 15(2/12) = 5/2 = 2 1/2
You will need 2 1/2 cups of zucchini to feed 15 people with the same recipe.
25% of 24
Can you show working out
All different methods to see which is easy or better for me
Answer:
---
Step-by-step explanation:
I'm not showing you all of them, but this one is very simple.
You convert the percent(25%) to a decimal(0.25), then multiply it by the whole number(24). So simple, I got it all in one sentence.
0.25x24=6
25% of 24 is 6.
---
hope it helps
Find the missing side. Round to the nearest tenth
Answer:
10.1
Step-by-step explanation:
we want to find the adjacent side given the opposite side
looking through SOHCAHTOA
Tan is the appropriate angle to use
Tan 62 = opposite / adjacent
1.881 = 19 / x
x = 19 / 1.881 = 10.1
tell me the tight answer you get brianliest
Answer:
1,A 2:C
Step-by-step explanation:
Answer:
Addition for 7
-42 + 42 = 0 by adding 42 you get rid of the -42
multiplication for number 8,
x/6 x 6 = x, always do the opposite of their operation for every question like these.
the population of a deer in the national park in model by the equation P = 300e^(it). If the population of the deer is 400 after 2 years, find the value of k. Round your answer to the nearest hundredth. NO LINKS!!!
Answer:
k ≈ 0.14
Step-by-step explanation:
Given
P = 300 [tex]e^{kt}[/tex]
Substitute P = 400 and t = 2 into the equation
400 = 300 [tex]e^{2k}[/tex] ( divide both sides by 400 )
[tex]e^{2k}[/tex] = [tex]\frac{4}{3}[/tex] ( take ln of both sides )
ln [tex]e^{2k}[/tex] = ln ([tex]\frac{4}{3}[/tex] )
2k = ln ([tex]\frac{4}{3}[/tex] ) ( divide both sides by 2 )
k = [tex]\frac{ln\frac{4}{3} }{2}[/tex] ≈ 0.14 ( to the nearest hundredth )
Can Someone Please Help Me Asap
Answer:
105.3
Step-by-step explanation:
cos(70)= 36/x
x=36/cos(70)
x=105.256958406
x~105.3
