Answer:
[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]
Step-by-step explanation:
Data given and notation
[tex]\bar X=67[/tex] represent the sample mean
[tex]s=12[/tex] represent the sample standard deviation
[tex]n=16[/tex] sample size
[tex]\mu_o =60[/tex] represent the value that we want to test
t would represent the statistic (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 60, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 60[/tex]
Alternative hypothesis:[tex]\mu > 60[/tex]
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]
The price of a watch was increased by 10% to £660. What was the price before the increase?
Answer:
£600
Step-by-step explanation:
First take if 110% equals to £660 what about 100%
100×660 =66000 ÷ 110 =£600
The original price of the watch, before the 10% increase, was £600.
Explanation:The price of a watch was increased by 10% to £660, and we are asked to find the price before the increase. We can solve this problem by considering that the increased price is 110% of the original price. To calculate the original price, let's set up the equation:
660 = 1.10 * Original Price
To solve for the Original Price, we divide 660 by 1.10:
Original Price = £660 / 1.10
This gives us the original price of the watch which is £600.
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A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles, B of water the machine can fill in m minutes.
Answer:
B x m
Step-by-step explanation:
Example: 75 x minutes
So no matter how much bottles you have, you just have to multiply the minutes.
Answer:I think it would be 75 divided by b = m
Step-by-step explanation:
Using the Zero Product Property, solve for the x-values given (x-2)(x+3)=0.
Answer:
x = 2 or -3
Step-by-step explanation:
The product will be zero when one of the factors is zero.
First factor:
x - 2 = 0
x = 2 . . . . . add 2 to both sides of the equation
Second factor:
x + 3 = 0
x = -3 . . . . .subtract 3 from both sides of the equation
The values of x that solve this equation are x = 2 and x = -3.
Kendra needs 2 3/4 cups of flour for cookies, 4 1/2 cups of flour for bread, and cup of flour 2/3 for biscuits , How much flour does she need in all?
Answer:
7 11/12
Step-by-step explanation:
amount of the flour
= 2 3/4 + 4 1/2 + 2/3
= 11/4 + 9/2 + 2/3
= 33/12 + 54/12 + 8/12
= 95/12
= 7 11/12
make as the brainliest
Answer:
Wofford College
Step-by-step explanation:
A principal gathered data about the distance, in miles, that his teachers and bus drivers live from school. The box plots below show these data.
Answer:
We choose C
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo
Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.
From the picture, we can find that:
The interquartile range of the bus drivers is: 20 -10 = 10 The interquartile range of the teachers is: 30 -15 = 15So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
We choose C
Answer:
Step-by-step explanation:
The Kamp family has twins, Rob and Rachel. Both Rob and Rachel graduated from college 2 years ago, and each is now earning $50,000 per year. Rob is an engineer. The mean salary for engineers with less than 5 years’ experience is $60,000 with a standard deviation of $5,000. Rachel works in the retail industry, where the mean salary for executives with less than 5 years’ experience is $35,000 with a standard deviation of $8,000.
Answer:
$38,000 is correct
Step-by-step explanation:
just took it
The z value is 1.875.
To compare Rob's salary as an engineer to the mean salary for engineers with less than 5 years of experience, we need to find the z-score of Rob's salary.
The z-score formula is
z = (x - μ) / σ,
where x is the given value,
μ is the mean, and
σ is the standard deviation.
Plugging in the values, we get z = (50,000 - 60,000) / 5,000 = -2.
For Rachel's salary as an executive in the retail industry, we use the same process.
The z-score formula is z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get z = (50,000 - 35,000) / 8,000 = 1.875.
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What is a tessalation
Answer:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Step-by-step explanation:
You went to the mall with $52.50. You bought three shirts that each cost x
dollars. Which expression represents the amount of money, in dollars,
that you had left after you bought the shirts? *
6. 4ab + 13b
Can someone help me find the andwers
Answer:
You cannot simplify this. One has ab, and one has only b. So that is the most simplified it can get.
Answer: There are no like terms.
Step-by-step explanation:
Carlos walked 16 of 20 of school days in February what is the value that is equivalent to the fraction of school days in February that Carlos walked to school . Math
Answer:
70%
Step-by-step explanation:
14 divided by 20
Answer:
6
Step-by-step explanation:
Using the circle below, if I double the radius in length, what affect does that have on the new circumference?
Answer:
it will also double the circumference
Step-by-step explanation:
c = 2πr
r' = 2r
c' = 2πr' = 2π x 2r = 4πr
A bread recipe calls for 2 cups of wheat flour and 3 cups of white flour. How much flour does the recipe call for
altogether?
Answer:
5
Step-by-step explanation:
3+2=5
Answer:
5 cups
Step-by-step explanation:
2 cups plus 3 cups
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle.
62 + 102 = 82
36 + 100 = 64
136 ≠ 64
Is her answer correct?
Answer
No, she should have added 62 and 82 and compared that to 102.
Answer:
The correct answer is C) No, she should have added 62 and 82 and compared that to 102.
Step-by-step explanation:
Her answer is incorrect because she did not follow the steps correctly, she should have added the two numbers. Good luck!
Monique is an interior design student. As part of her internship, she is redesigning a small kitchen for a client. She would like to expand the kitchen and add a dining area. Before creating sketches for the client, she imagines the new layout in her mind, most likely using __________.A. tacit knowledge.
B. a proposition.
C. the method of loci.
D. a depictive representation.
11: Jack is 10 years old.
Kylie is 17 years old.
Vanessa is 23 years old.
Kylie and Vanessa share £16 in the ratio of their ages.
Kylie gives 20% of her share to Jack.
Vanessa gives a quarter of her share to Jack.
How much money does Jack receive?
Answer:
£3.66
Step-by-step explanation:
17+23=40
40=16 what about 17
16×17=272÷40=£6.8
16-6.8=£9.2
20% of £6.8 = £1.36
1/4 of £9.2 = £2.3
1.36+2.3=£3.66
Convert the angle 0 = 230° to radians.
Answer:
230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
General Formulas and Concepts:
Trigonometry
Degrees to Radians Conversion: [tex]\displaystyle \frac{n\pi}{180}[/tex]
n is the degreesStep-by-step explanation:
Step 1: Define
Identify variables.
n = 230°
Step 2: Find Radians
Substitute in variable [Degrees of Radians Conversion]: [tex]\displaystyle \frac{230 \pi}{180}[/tex]Simplify: [tex]\displaystyle \frac{23 \pi}{18}[/tex]∴ 230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
---
Topic: Pre-Calculus
Unit: Trigonometry
need help on this math problem can someone help ax +by=cz
Answer:
a = (cx - by)/x
Step-by-step explanation:
ax + by = cz
ax = cz - by
a = (cx - by)/x
Can I get brainliest
1. A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in?
Answer:???
Step-by-step explanation:
Answer:
As the stake is 3 m long we will take it as the radius of the circle and find the area as per:
22/7*3*3=22/7*9=198/7m^2
198/7 metre square.
Use the given qualitative data to construct the relative frequency distribution. The 2545 people aboard a ship that sank include 406 male survivors, 1651 males who died, 362 female survivors, and 126 females who died.Complete the relative frequency distribution below. Relative Frequency Category Male survivors % Males who died % Female survivors % Females who died % (Round to one decimal place as needed.)
Answer:
The data that we have is:
total people: 2545
male survivors: 406
male who died: 1651
total males: 406 + 1651 = 2057
female survivors: 362
female who died: 126
total females: 362 + 126 = 488.
We want to know:
for the percentages, we must calculate the quotient between the total numbers of the set, and the number in the particular category we are looking for.
% male survivors = (number of male survivors/total number of males)*100%.
= (406/2057)*100% = 19.73%
% male who died = (1651/2057)*100% = 80.2%
% female survivors = (362/488)*100% = 74.18%
% female who died = (126/488)*100% = 25.82%
There are two peice pf gold and silver alloy. The ratio between the gold and silver in the first piece is 2:3, in the second peice 3:7. If we want to have 8 gram of gold and silver alloy with gold-silver ratio 5:11 how much of each peice of alloy is needed.
Answer:
1 grams of one of the alloy; and 7 grams of the other corresponding alloy.Step-by-step explanation:
The ratio between the gold and silver in the first piece = 2:3
The ratio between the gold and silver in the second piece =3:7
The ratio in the mixture = 5:11
We want to have 8 gram of the new mixture.
Let the gram of alloy taken from the first piece=x
Therefore: gram of alloy would be taken from the second piece=(8-x)
This gives:
[tex]\dfrac{2}{5}x+ \dfrac{3}{10}(8-x)=\dfrac{5}{16}*8[/tex]
We simplify the equation above for the value of x.
[tex]\dfrac{2x}{5}+ \dfrac{3(8-x)}{10}=\dfrac{5}{2} \\\dfrac{4x+24-3x}{10}=\dfrac{5}{2}\\\dfrac{x+24}{10}=\dfrac{5}{2}\\2x+48=50\\2x=50-48\\2x=2\\x=1[/tex]
Therefore to create 8 gram of gold and silver alloy with gold-silver ratio 5:11, we take 1 grams of one of the alloy and 7 grams of the other alloy.
Suppose you wanted to change the state’s constitution to require public financing for all campaigns. If you were relying on professional signature gatherers (who charge at least $1.50 per signature), what is the minimum amount of money you could reasonably expect to spend in order to qualify this amendment for the ballot?
Answer: $1.5 millions
Step-by-step explanation:
Since the population is in millions and a million is like a fraction many millions.
Therefore, the minimum amount of money you could reasonably expect to spend in order to qualify for this amendment for the ballot is $1.5 millions
What are the factors of x2 + 3x - 4?
(x + 4) and (x - 4)
(x + 3) and (x-4)
(x + 4) and (x - 1)
(x + 3) and (x - 1)
Answer:
C. (x + 4) and (x - 1)
Step-by-step explanation:
The middle number is 3 and the last number is -4.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 3
Multiply together to get -4
Can you think of the two numbers?
Try -1 and 4:
-1+4 = 3
-1*4 = -4
Fill in the blanks in
(x+_)(x+_)
with -1 and 4 to get...
(x + 4) and (x - 1)
In 2002, a reproductive clinic reported 41 live births to 152 women under the age of 38, but only 4 live births for 86 clients aged 38 and older. Is there evidence of a difference in the effectiveness of the clinic's methods for older women? Complete parts a through c. Use alphaequals0.05.
Answer:
Difference is (0.181671, 0.263529)
We are more than 95% confident that the true percentage of life births for women under 38 years of age is between 18.17% and 26.35% higher than the true population of live births of women aged 38 or older.
Step-by-step explanation:
We are given;
x1 = 41
n1 = 152
x2 = 4
n2 = 86
Thus,
Sample proportion 1; p'1 = 41/152 = 0.2697
Sample proportion 2; p'2 = 4/85 = 0.0471
For confidence level, 1 - α = 1 - 0.05 = 0.95, using the z-table i attached under the column of z_α/2,we have
z_α/2 = 0.96
The end points of the confidence intervals for p1 - p2 are;
(p'1 - p'2) - z_α/2√[(p'1(1 - p'1)/n1) + (p'2(1 - p'2)/n2)
And
(p'1 - p'2) + z_α/2√[(p'1(1 - p'1)/n1) + (p'2(1 - p'2)/n2)
The first one is calculated as;
(0.2697 - 0.0471) - 0.96√[(0.2697(1 - 0.2697)/152) + (0.0471(1 - 0.0471)/86)
.= 0.2226 - 0.040929 = 0.181671
The second one is calculated as;
(0.2697 - 0.0471) + 0.96√[(0.2697(1 - 0.2697)/152) + (0.0471(1 - 0.0471)/86)
.= 0.2226 + 0.040929 = 0.263529
Thus, we are more than 95% confident that the true percentage of life births for women under 38 years of age is between 18.17% and 26.35% higher than the true population of live births of women aged 38 or older.
BRAINLIEST if right!
What is the equation of the line with a y-intercept of −10 and a slope of 3?
Answer:
y = 3x-10
Step-by-step explanation:
The slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
The slope is 3 and the y intercept is -10
y = 3x-10
proving the converse of the parallelogram side theorem
Answer:
* LOOK AT THE PICTURE's*
I hope this helps and is the right one
The converse of the parallelogram side theorem states, If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
To prove this statement, we will assume that the opposite sides of a quadrilateral are congruent and demonstrate that it must be a parallelogram.
If both the opposite sides are parallel then we can easily prove that a parallelogram
Given: Quadrilateral PQRS, where PQ is congruent to RS and PR is congruent to QS.
To prove: PQRS is a parallelogram.
Proof:
Since PQ is congruent to RS (given), the segment PQ is parallel to the segment RS by the converse of the corresponding sides of congruent triangles are congruent (CPCTC). Since PR is congruent to QS (given), the segment PR is parallel to the segment QS by CPCTC.
Now we have both pairs of opposite sides of PQRS parallel, which satisfies the definition of a parallelogram.
Therefore, by proving that both pairs of opposite sides are PQRS parallel, we have shown that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
This completes the proof of the converse of the parallelogram side theorem.
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please hellllllllppppppppppppppppppppppppppp
Answer:
[tex]21^{10}[/tex]
Step-by-step explanation:
First, multiply the 3 and the 7 together, and then "multiply" the exponents -8 and 3. (However, when "multiplying exponents, you're really just adding them together: -8 + 5)
([tex]21^{-5}[/tex])^2
Then, multiply the -5 and -2 together, giving you:
[tex]21^{10}[/tex]
How can you find f(2) if f(x)=−3x2−7?
Step-by-step explanation:
F(2)=3(2)²-7
=5
................
Answer:
Square 2. Multiply the result by -3, and then subtract 7.
Step-by-step explanation:
The answer is basically the explanation of the answer. You want to replace x with 2 then square it. You will have 4. Multiply 4 by -3 and you will have -12 then subtract it by 7 and you'll get the answer to f(x). The answer is the steps. Not the 'answer' answer. Hope this helps! (I did this question, and I got it right.)
Sophia factored 81y^6 as (9y^3)(9y^2) Ahmed factored 81y^6 as (3y^6)(27y) Which of them factored 81y^6 correctly?
To find if either of them are correct just multiply each of them:
(9y^3)(9y^2)= (9)(9)(y^3)(y^2)
=81y^5
Sophia is incorrect.
(3y^6)(27y)=(3)(27)(y^6)(y)
=81y^7
Ahmed isn't correct either!
Both the persons Sophia and Ahmed do not factor in the expression correctly.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that, Sophia factored 81y⁶ as (9y³)(9y²) and Ahmed factored 81y⁶ as (3y⁶)(27y).
We have to find the correct factored form,
= (9y³)(9y²)
The expression is to be arranged in order to find the understand the property of exponent as,
=(9×9)(y³.y²)
=(81)(y³⁺²)
=81y⁵
Thus, both the persons Sophia nor Ahmed do not factor in the expression correctly.
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Please help me with this
Step-by-step explanation:
Putting values of c and r
4 + 4(10) - 3(10 - 3)
4 + 40 - 3(7)
44 - 21
23
Which of the following is the inverse of y = 6 Superscript x?
y = log Subscript 6 Baseline x
y = log Subscript x Baseline 6
y = log Subscript one-sixth Baseline x
y = log Subscript 6 Baseline 6 x
Answer:
Option A
Step-by-step explanation:
your welcome = )
The inverse of the function y = 6ˣ is y = log₆(x), which means option A is correct.
To find the inverse of the function y = 6ˣ, we need to swap the roles of x and y and then solve for y. The steps to find the inverse are as follows:
Start with the original function: y = 6ˣ
Swap x and y:
[tex]x = 6^{y}[/tex]
To solve for y, take the logarithm of both sides using the same base (in this case, base 6):
log₆x = log₆([tex]6^{y}[/tex])
Since [tex]log_{b} (b^{y} )[/tex] = y, we get: y = log₆x
Therefore, the inverse function is y = log₆x.