Answer:
11
Step-by-step explanation:
Add 4 to both sides to get rid of -4 or if you want think of it as moving -4 to the other side and turning it into positive if its negative and negative if its positive
r=11
In Mrs. Austin's science class, 37.5% of the students have compleated their science project. Of the remaining students, 40% have compleated only half of their science project. If there are 32 students in Mrs. Austin's science class, how many of these students have compleated half of their science project?
well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.
now, of those 62.5% fellows only 40% have finished only half of it, how many are those?
well, what's 62.5% of 32? what's 40% of that much?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 31 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,060, while the mean attendance on Wednesday evening is calculated as 5,390. The known population standard deviation for attendance on Tuesday evening is 540 and the known population standard deviation for attendance on Wednesday evening is 480. Which of the following is the appropriate conclusion at the 5% level of significance?
a. Conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.
b. Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.
c. Do not conclude that the mean attendance differs since the p-value = 0.0067 < 0.05.
d. Do not conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.
Answer:
b. Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.
Step-by-step explanation:
Before testing, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of 31 weeks. The mean attendance on Tuesday evening is calculated as 5,060, with a population standard deviation of 540.
This means that:
[tex]\mu_{T} = 5060, s_T = \frac{540}{\sqrt{31}} = 97[/tex]
The mean attendance on Wednesday evening is calculated as 5,390, with standard deviation of 480.
This means that:
[tex]\mu_{W} = 5390, s_W = \frac{480}{\sqrt{31}} = 86.21[/tex]
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.
At the null hypothesis we test if there is no difference, that is:
[tex]H_0: \mu_T - \mu_W = 0[/tex]
At the alternate hypothesis, we test if there is difference, that is:
[tex]H_a: \mu_T - \mu_W \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples collected:
[tex]X = \mu_T - \mu_W = 5060 - 5390 = -330[/tex]
[tex]s = \sqrt{s_T^2+s_W^2} = \sqrt{97^2+86.21^2} = 129.77[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-330 - 0}{129.77}[/tex]
[tex]z = -2.54[/tex]
Pvalue of test and decision:
The pvalue of the test is finding the probability of the sample mean difference differing by 0 by at least 330, that is, P(|z| > 2.54), which is 2 multiplied by the pvalue of z = -2.54.
Looking at the z-table, z = -2.54 has a pvalue of 0.0067.
2*0.0067 = 0.0134
The pvalue of the test is 0.0134 < 0.05, which means that there is evidence that the mean attendance differs. The correct answer is given by option b.
please answer in full process question
In the given figure l ||m and p || q. Find the measure of angles √1,2,3,4
Step-by-step explanation:
angle 1=68°
angle 3 = 68°
angle 2= 180-68= 112°
angle 4 = 180-68= 112°
i will give Brainiest if you are right
Answer:
H is the answer because 15/32 is the largest so it is in the back
Answer:
J. [tex]\frac{9}{32}, \frac{5}{16},\frac{3}{8},\frac{7}{16},\frac{15}{32},\frac{1}{2}[/tex]
Step-by-step explanation:
7/16 = .4375
1/2 = .5
3/8 = .375
9/32 = .28125
5/16 = .3125
15/32 = .46875
Please help me with this math question if u answer with no file link I will mark brainlist!!
A rectangle has coordinates W (1, -2), X (7,-2), Y (7,-6), and Z (1, -6).
The length of WXYZ is
units, and the width is
units.
7.6
7,2
6,4
5,3
Answer:
6, 4
Step-by-step explanation:
W to X : 7 - 1 = 6
W to Z : (-2) - (-6) = 4
Answer:
6,4
Step-by-step explanation:
One way is to calculate the distance between W and X, and X and Y to find the length and width.
The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
plug W(1,-2) and X(7,-2) in to get the length
[tex]\sqrt{(1-7)^2+(-2-(-2))^2}=\sqrt{(-6)^2 +0^2}=\sqrt{36} =6[/tex]
plug X(7,-2) and Y(7,-6) to get the width
[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]
Original price of concert tickets: $101.00
Markup: 21%
What's the selling price of the concert tickets?
Answer:
122.21
Step-by-step explanation:
So our orginal value is 101 dollars,
Markup is increase in value.
The markup in this problem is 21%
We can thikn of this as 121%.
So to find the markup price, we must multiply 121% by 101.
We can thibk of 121% being myltiplying by 101 as:
1.21*101
This will get you:
122.21
So this is your answer!
Hope this helps! :)
80 items were sold, bringing in $6,900 in receipts. Some items were sold at a discount for $75 each and some others were sold at full price for $90 each. How many were sold at discount and how many at full price?
Answer:
50 items were sold for $75
35 items were sold for $90
Step-by-step explanation:
75 x 50 = 3750
90 x 35 = 3150
3750 +3150 = 6,900
Researchers for a company that manufactures batteries want to test the hypothesis that the mean battery life of their new battery is greater than the known mean battery life of their older version. The researchers selected random samples of 32 of the new batteries, subjected the batteries to continuous use, and determined the mean and standard deviation of the battery lives in the sample. Which of the following is an appropriate test for the researchers' hypothesis?
a. A one-sample z-test for a population mean.
b. A one-sample t-test for a population mean.
c. A one-sample z-test for a population proportion.
d. A matched-pairs t-test for a mean difference
e. A two-sample t-test for a difference between means
(b) one-sample t-test for a population mean
ur welcome :D
The most appropriate test to be used here would be a b. A one-sample t-test for a population mean.
Reasons to use one-sample t-test for a population mean.One sample t-test is used when one wants to compare the mean of a population to another mean for statistical difference which is what the researchers hope to do here in comparing the mean battery life of a new battery to an old one.
A population mean will also be used because the population standard deviation is not given.
In conclusion, option B is correct.
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Determine the correct set up for solving the equation using the quadratic formula.
Answer: B
Begin by simplifying the given equation, so it's rearranged into standard form. Move all the terms onto one side, so they equal 0. This would result with [tex]4x^{2}[/tex]-3x-9=0. Quadratic formula is (-b±√(b²-4ac))/(2a). Standard form follow this variable format: [tex]ax^{2}[/tex]+bx+c. Use the numbers that correspond with each variable to substitute them into the quadratic formula. This would be
(-(-3)±√(-3²-4(4)(-9)/2(4).
A data set is made up of the values 5, 6, 9, 12, and 18.
The table shows the distance between each value and the mean of 10.
Answer:
A. 4
Step-by-step explanation:
To find the Mean Absolute Deviation (MAD) of a data, the following steps are usually taken:
1. Find the mean
2. Find the distance between each data value and the mean
3. Find the sum of the distances
4. Divide the sum of the distances by the number of data value given
Step 1 to 3 has been solved already from the table given.
The sum of the distances = 20
number of data value = 5
Therefore,
MAD = 20/5 = 4
a) Find the total mass in kilograms of 3500 books, each with mass 800.
b) If the total mass of 8000 apples is 1.04 tonnes, what is the average mass of one apple?
A) Total mass of 3500 books is 2,800 kilograms.
B) The average mass of one apple is 130 grams.
A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:
Total mass = (3500 books) * (800 grams/book)
= 2,800,000 grams
= 2,800 kilograms
Therefore, the Total mass of 3500 books is 2,800 kilograms.
B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:
Average mass = (1.04 tonnes) / (8000 apples)
= 130 grams/apple
Therefore, the average mass of one apple is 130 grams.
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In the construction of bridges, engineers use a formula to help
determine the allowable stress on a bridge rocker, a component of the
bridge that handles the stress and weight placed on the pavement of the
bridge. The engineers use the formula F =11/300d (F − 13), where F is the
strength of the steel in kilopound per square inch and d is the diameter
of the rocker in millimeters.
Solve the formula F =11/300d (F − 13) for d.
From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))
How to change the subject of the formula?
We are given the engineers formula as;
F = (¹¹/₃₀₀)d(F - 13)
Where;
F is the strength of the steel in kilopound per square inch.
d is the diameter of the rocker in millimeters.
From the given formula, we can start by;
Multiply both sides by 300 to get;
300F = 11d(F - 13)
Divide both sides by 11(F - 13) to get;
d = 300F/(11(F - 13))
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Consider this right triangle with given measures.
What is the length of the unknown leg of the given right
triangle?
O 3ft
O vo ft
O 39 ft
O 89 ft
Answer:
[tex] \sqrt{39} [/tex]
Step-by-step explanation:
5
[tex]5 {}^{2} + x {}^{2} = 8 {}^{2} \\ 25 + x {}^{2} = 64 \\ x {}^{2} = 64 - 25 \\ x {}^{2} = 39 \\ x = \sqrt{39} [/tex]
The length of the unknown length is √39 ft if the other lengths are 5 ft and 8 ft in the right angle triangle.
What is a right-angle triangle?It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.
Let's suppose the unknown length is x ft
From the Pythagoras theorem:
[tex]\rm hypotenuse^2= perpendicular^2+ base^2[/tex]
[tex]8^2 = 5^2 +x^2[/tex]
64 = 25 + x²
x = √39 ft
Thus, the length of the unknown length is √39 ft if the other lengths are 5 ft and 8 ft in the right angle triangle.
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Below are graphs of several functions. Which functions have the specified domain and range ? There may be more than one correct answer
For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.
What do you mean by function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
What are domain and range of the function?A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.
domain : (x | x 3/2)
range : (-∞ , 2)
For these values, Option B , C and E holds that they exists when x 3/2 and it's output that is y exists between (-∞ , 2).
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Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.
Line Speed Number of Defective Parts Found
20 23
20 21
30 19
30 16
40 15
40 17
50 14
50 11
Required:
a. Use the least squares method to develop the estimated regression equation (to 1 decimal).
b. Predict the number of defective parts found for a line speed of 25 feet per minute.
Answer:
a. y = 27.5 - 0.3X
b. 20
Step-by-step explanation:
y = a + bX
usin the table in the attachment i added, we so for the regression equaion
n = 8
∑xy = 4460
∑x = 280
∑y = 136
∑x²= 10800
[tex]b=\frac{8(4460)-(280)(136)}{8(10800)-280^{2} } \\b=\frac{35680-38080}{86400-78400} \\b=\frac{-2400}{8000} \\b = -0.3[/tex]
from here we solve for a
[tex]a= \frac{136-(-0.3)(280)}{8} \\a =\frac{136+84}{8} \\a=\frac{220}{8} \\a = 27.5[/tex]
a. the estimated regression equation
y = 27.5 - 0.3X
b. at x = 25
y = 27.5 - 0.3(25)
y = 20 is the number of defective parts.
of the 8 friends sitting around the table at lunch,6 brought their lunch from home.Which grid represents the percent of the friends brought their lunch from home
Answer:
6/8 =1.3333... or 33.3%
Step-by-step explanation:
Answer:
33.4 %
Is what I think I am not very sure but try it out hope this helped!
Car Travels
In this new car your family can drive on a trip at 50 miles per hour. The
distance D you go is a of how many hours T you drive
function:d=50T if you drive for 125 miles how long would it take you to drive
stock splits will not..
Answer:
Thank you for the points...
Step-by-step explanation:
If a < b, c > b, d > c, and c < e < d, order the letters from least to greatest
The order of a,b,c,d,e from least to greatest is a<b<c<e<d.
What is order of numbers?Order is basically a series which contains a particular operation like addition, subtraction, multiplication,division and size of numbers may be from greater to least and least to greater numbers.
How to arrange a order?We have been given a<b,c>b,d>c, and c<e<d and we have to order the letter from least to greatest.
a is greater than b, c is greater than b so a is also lesser than c. So,a<b<c will be order of a,b and c. Now we include d in the order. because c is greater than a and b but less than d so the order increases as under:
a<b<c<d. e lies between c and d so we will write e in between c and d in order. Final order will be a<b<c<e<d.
Hence the order of a,b,c,d,e from least to greatest is a<b<c<d<e.
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Which graph represents the solution to 1/7 m < - 1/22
The graph representing the solution will be of the form a line tending towards left from the point -7/22.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Here the given inequality is less than inequality.
1/7 m < -1/22
Dividing both sides by 1/7, we get,
m < -1/22 ÷ 1/7
m < -1/22 × 7/1
m < -7/22
Hence the graph of the solution will be of the form a straight line tending leftwards from -7/22.
Hence the graph of the given inequality is a straight line tending leftwards from -7/22.
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Find the equation of the line below. If necessary, use a slash ( / ) to indicate a division bar.
Answer:
y=4x
Step-by-step explanation:
Rise= 8
Run= 2
8/2 = 4/1 = 4
y=(slope)x+(y intercept)
y=4x+0
y=4x
y=4x
Complete table with the Y-values for the equation y=ײ+1
The complete table of values of the function is
x 0 1 2 3
y 0 2 5 10
How to complete the table of values of the function?From the question, we have the following parameters that can be used in our computation:
The equation of the function is given as
y = x² + 1
The above function is a quadratic function
This is so because it has the following representation
y = ax² + bx + c
When this function is compared to the equation y = x² + 1, we have the following notations
a = 1
b = 0
c = 1
From the incomplete table of values, we have the x values to be
x = 1, 2, 3
Substitute x = 1, 2, 3 in the equation y = x² + 1
So, we have
When x = 1, y = (1)² + 1 = 2
When x = 2, y = (2)² + 1 = 5
When x = 3, y = (3)² + 1 = 10
When these values are represented on a table, we have
x 0 1 2 3
y 0 2 5 10
The above represents the complete table
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Complete question
Complete table with the Y-values for the equation y=ײ+1
x 0 1 2 3
y 0
What is the distance between the points (-4, 8) and (10,-3)?
Answer:
17.8
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
then plug it in
[tex]d=\sqrt{(10+4)^2+(-3-8)^2}[/tex]
then solve inside the parentheses
[tex]d=\sqrt{(14)^2+(-11)^2}[/tex]
then simplify
[tex]d=\sqrt{196+121}[/tex]
keep simplifying
[tex]d= \sqrt{317}[/tex]
solve the square root
[tex]d=17.80449381[/tex]
round
[tex]d=17.8[/tex]
- The length of a rectangle is 2 less than 5 times its width. The area of the rectangle is 39 km².
Find the length and width of the rectangle.
Answer:
Length is 13 and width is 3
Step-by-step explanation:
First find an equation that represents this situation.
39 = w * (5w-2)
This works because 39 (the total area) is w (the width) times 5w - 2 (the length). So solve for w.
39 = w * (5w-2)
First, distribute the w over the terms in parentheses
39 = 5w^2 - 2w
Then, subtract (5w^2 - 2w) from both sides.
39 - 5w^2 - 2w = 0
Factor the left side of the equation:
(−5w−13)(w−3)=0
Then set each factor equal to zero.
−5w−13 = 0
Add 13 to both sides, then divide both sides by -5 to isolate w. This leaves you with w = -13/5
Then the other factor:
w−3 = 0
Add 3 to both sides. You're left with w = 3.
So w is either -13/5, or 3. And since the width can't be negative, it is 3.
Now to find the height, plug 3 into the equation we had from earlier:
39 = w * (5w-2)
Substitute w into the equation:
39 = (3) * (5(3)-2)
39 = 3 * (15 - 2)
39 = 3 * (13)
Because 3 * 13 is equal, 13 is the length.
Can y’all help me on question 15?!
Answer:
J = 33
Step-by-step explanation:
43 - 2k = 33
43 - 10 = 33
33 = 33
is 7.787878— a rational number?
Answer:
yes it is a rational number.
Step-by-step explanation:
To make a solution for an experiment, Gunther needs to add 40 g of a solute to 100 g of water. When making the
solution at room temperature, he could only add 34 grams before the solute settled out.
What could he do to dissolve the remaining 6 grams of the solute?
Put the solution in an ice bath, dissolve the solute, and let the solution return to room temperature.
O Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled out.
O Add more water, boil the solution, and dissolve the solute until the some of the water evaporates.
O Keep the solution at room temperature, add more water, and dissolve the excess solute.
Answer:
Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled....(B)
Step-by-step explanation:
hope this helps
Gunther could dissolve the remaining 6g by heating the solution to dissolve the solute, and let the solution cool verifying nothing settled out.
Solubility of a substance refers to the amount of the substance that dissolves in a given amount of water. The most important factor that affects solubility is the temperature of the system. When the temperature is increased, more solute can be dissolved in the solvent.
Since Gunther needs to add 40 g of a solute to 100 g of water but only 34 grams were added before the solute settled out at room temperature. He could dissolve the remaining 6g by heating the solution to dissolve the solute, and let the solution cool verifying nothing settled out.
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A marketing executive surveyed 1,000 shoppers at a grocery store to determine the highest price shoppers are willing to pay for a gallon of ice cream. His data is show in the table.
Based on the data, of 10,000 shoppers, which BEST estimates the number of shoppers that would be willing to pay $8.00 for a gallon of ice cream.
If you cannot see, zoom in!
Don’t answer if you don’t know the answer. Whoever answers correctly will get Brainliest! :)
Answer:
C
Step-by-step explanation:
You multiply times 10
help me my future depends on it
Answer:
Step-by-step explanation:
Name the image of p (9, 1.5) after being translated along the vector <3, -0.5>
The image for P(9, 1.5) after Translation is P'( 12, 1).
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
P(9, 1.5) with Translating Vector (3, -0.5).
So, Applying the Translation we get
P(9 + 3, 1.5 + (-0.5))
= P(12 , 1.5- 0.5)
= P(12, 1)
hence, the image is P'( 12, 1).
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