Answer: QS is 76
Step-by-step explanation:
Since R is the midpoint of QS:
1) 2x+16 = 5x-17
2) 2x+16+17 = 5x-17+17
3) 2x-2x+33 = 5x-2x
4) 33 = 3x
5) 11 = x
Since the sum of QR and RS equal QS:
1) (2·11+16)+(5·11-17) = QS
2) 22+16+55-17
3) 76 = QS
A professor counted the number of words students used to answer an essay question. Create a ranked frequency distribution of these data.
245 261 289 222 291 289 240 233 249 200
A ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value.
The given data set is 245, 261, 289, 222, 291, 289, 240, 233, 249, and 200. To create a ranked frequency distribution of this data set, we first need to sort it in ascending or descending order. Let's sort it in ascending order:200, 222, 233, 240, 245, 249, 261, 289, 289, 291 Next, we need to count the frequency of each value. We can do this by going through the data set and counting how many times each value occurs. Here is the frequency distribution table:Value Frequency 200 1222 1233 1240 1245 1249 1261 1289 2291 1 From this table, we can see that the most frequent value is 289, which occurs twice. We can also see that the least frequent values are 200, 222, 233, and 240, which each occur only once.
In conclusion, a ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value. This allows us to see which values are most and least frequent in the data set.
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At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 0.95 centimeter and a standard deviation of 0.02 centimeter. A random sample of 4 computer chips is taken. What is the variance for the sample mean?
The variance for the sample mean is 0.0001 cm².
To find the variance for the sample mean of 4 computer chips with a mean of 0.95 centimeters and a standard deviation of 0.02 centimeters, you can follow these steps:
1. Note the population mean (µ) = 0.95 cm and population standard deviation (σ) = 0.02 cm.
2. Identify the sample size (n) = 4.
3. Calculate the variance for the sample mean using the formula: variance of sample mean = (σ²) / n.
In this case, the variance of the sample mean is:
Variance of sample mean = (0.02 cm)² / 4 = 0.0004 cm² / 4 = 0.0001 cm².
So, the variance for the sample mean of the 4 computer chips is 0.0001 cm².
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What are the domain and range of the function f(x)=-3(x-5)squared +4?
Answer:
Domain= neg infinite, pos infinite
range= neg infinite, 4
Kelly ran 26.8 miles over 4 days at the beach. She ran the same number of miles each day. How far did she run each day?
Answer:
Easy it 6.4 you get it by dividing.
Step-by-step explanation:
On the unit circle, where 0 < theta < or equal to 2pi, when is tan theta undefined?
A. Theta=pi and theta=2pi
B. sin theta = cos theta
C. theta = pi/2 and theta=3pi/2
D. sin theta = 1/cos theta
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.
To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).
Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.
At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.
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if you have minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency?
Yes, if you have minimums and maximums that are several standard deviations away from the rest of the data observations, medians would be the best measure of central tendency.
Having minimums and maximums that are far away (several standard deviations away from the mean) from the rest of the data observations, medians would be the best measure of central tendency. This is because, when there are outliers or extreme values in a dataset, the mean can be influenced and it may not be an accurate representation of the central tendency.
However, the median is not affected by extreme values or outliers since it only depends on the middle value of the dataset. Therefore, if the dataset has outliers, it is better to use the median as a measure of central tendency to provide a more accurate representation of the data.
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Graph (on paper). State the domain and range. h(x)=∥x−5∥ Upload Question 2 Graph (on paper). State the domain and range. f(x)=∥x+1∥. Upload Graph (on paper). Identify the domain and range. y=2∣x∣ Upload Question 4 Graph (on paper). Identify the domain and range. y=∣−3x∣
1. Graph of h(x) = |x - 5|: Domain: R, Range: [0, +∞).
2. Graph of f(x) = |x + 1|: Domain: R, Range: [0, +∞).
3. Graph of y = 2|x|: Domain: R, Range: [0, +∞).
4. Graph of y = |-3x|: Domain: R, Range: [0, +∞).
Graph of h(x) = |x - 5|:
The graph is a V-shaped graph with the vertex at (5, 0).
The domain of the function is all real numbers (-∞, +∞).
The range of the function is all non-negative real numbers [0, +∞).
Graph of f(x) = |x + 1|:
The graph is a V-shaped graph with the vertex at (-1, 0).
The domain of the function is all real numbers (-∞, +∞).
The range of the function is all non-negative real numbers [0, +∞).
Graph of y = 2|x|:
The graph is a V-shaped graph with the vertex at (0, 0) and a slope of 2 for x > 0 and -2 for x < 0.
The domain of the function is all real numbers (-∞, +∞).
The range of the function is all non-negative real numbers [0, +∞).
Graph of y = |-3x|:
The graph is a V-shaped graph with the vertex at (0, 0) and a slope of -3 for x > 0 and 3 for x < 0.
The domain of the function is all real numbers (-∞, +∞).
The range of the function is all non-negative real numbers [0, +∞).
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find the radian measure of an angle at the center of a circle with radius 77.0 cm that intercepts an arc length of 128 cm
The radian measure of the angle at the center of the circle is approximately 1.6623 radians.
We are given that the radius of the circle is 77.0 cm and the length of the intercepted arc is 128 cm. We need to find the radian measure of the angle at the center of the circle.
To solve this problem, we use the formula relating the angle at the center of a circle, the radius of the circle, and the arc length intercepted by the angle.
The formula is given byθ = s/rwhereθ = angle at the center of the circle in radians s = arc length intercepted by the angle r = radius of the circle Substituting the given values, we getθ = 128/77.0 = 1.6623 radians (rounded to four decimal places)
Therefore, the radian measure of the angle at the center of the circle is approximately 1.6623 radians.
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1/4(12)^2=
what is the answer?
Answer:
36
Step-by-step explanation:
I hope this helps! have a good day / night:)
Answer:
36
Step-by-step explanation:
1/4*12²
= 1/4*12*12
= 36
Jake made some basketball shots. he made 2pointers and 3pointers during his game
2x(4+6)
3x(1+2)
his claim said he did 2-pointers twice as 3-pointers because he is 4+6 is greater than 1+2. Explain that his claim is not correct even though 4+6 is greater than 1+2
Jake's claim that he made twice as many 2-pointers as 3-pointers based on the sums of the factors is invalid as it does not consider the number of shot attempts.
Jake's claim that he made twice as many 2-pointers as 3-pointers because 4+6 is greater than 1+2 is not correct. This is because the number of shots he made cannot solely be determined by the sum of the factors in each shot type.
It is possible for Jake to have made more 3-pointers despite the smaller sum of factors, as long as he attempted more shots from that range.
Therefore, without additional information about the number of attempts he made for each shot type, it is not valid to conclude that he made twice as many 2-pointers as 3-pointers solely based on the sums of the factors.
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Find the area and perimeter
Answer:
A=240 P=64
Step-by-step explanation:
A=240 because you take lxw and that gives you the answer
P=64 because you just add 12+12+10+10
Answer: The area is 240 and the perimeter is 64
Step-by-step explanation:
To get the area you need to do 20 x 12 = 240
And to get the perimeter you need to add up all the sides;
20 + 20 + 12 + 12 = 64
10) Find the least number that must be subtracted from the following numbers to make them perfect squares. a) 1098 b) 4498
Answer:
a. 9
b. 9.
Step-by-step explanation:
a) √1098 = 33.136
33^3 = 1089
So the answer is 1098 - 1089
= 9.
b) √4498 = 67.067
67^2 = 4489
Answer = 9.
Answer:
a). 9
b). 9
Step-by-step explanation:
a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.
√1089 = 33
33² = 33 × 33 = 1089
So the answer is 9.
b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.
√4489 = 67
67² = 67 × 67 = 4489
So the answer is 9.
Hope you understand ◉‿◉ (◠‿◕)
Give the domain and range of the relation.
The domain and the range of the given relation are respectively -3 < x < 4 & y = -5. So option B is correct.
What is Domain and Range ?The domain of a function is the set of all input values (which are known as independent variable) for which the function is defined and produces a valid output (dependent variable).
The range of a function is the set of all possible output values(dependent variable) of the function. It represents the set of all possible values of the dependent variable.
Given that,
A relation,
which is line segment,
It can be seen that the relation is valid only in the interval of -3 to 4 of x
and it is a constant parallel line and value of y is -5
So, the domain = (-3, 4)
the range = -5
Thus, the domain and range are (-3, 4) & -5
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Two researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same?
The two populations will be the same after
years.
Answer:
3 years
Step-by-step explanation:
Let y = number of orangutans, and let x = number of years.
For each study, the population, y, after x years is:
First study:
y = 784 - 25x
Second study:
y = 817 - 36x
We set the populations equal and solve for x, the number of years.
784 - 25x = 817 - 36x
Add 36x to both sides. Subtract 784 from both sides.
11x = 33
Divide both sides by 11.
x = 3
Answer: 3 years
The sum of two consecutive even integers is 16 less than three times the larger number. Find the integers.
Step-by-step explanation:
SOLUTION: the sum of two consecutive even integers is 16 less than three times the larger number. find the integers. 2x+2=3x+6-16 Subtract 2x from each side. 2=x-10 Add 10 to each side.
Suppose the midpoint of (AB) is M = (3,0). If point A has the coordinates of (-1,4), then what are the coordinates of B?
(1,2)
(-5,8)
ОООО
(7,-4)
О (-4,4)
Step-by-step explanation:
Hey there!
Here;
The one end is A(-1,4) and midpoint M(3,0).
Let another endpoint be B(x,y).
Using midpoint formula.
\((x,y) = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)
Put all values.
\((3,0) = ( \frac{ - 1 + x}{2} ,\frac{4 + y}{2} )\)
Since, they are equal, equating with their corresponding elements we get.
\(3 = \frac{ - 1 + x}{2} \)
6 = -1 +x
x= 7.
Again,
\(0 = \frac{4 + y}{2} \)
0 = 4+y
y = -4
Therefore the another endpoint is (7,-4).
So, answer is option C.
Hope it helps...
what are 5 expressions that are equivalent to 12x4
Answer:
6 x 8
48 x 1
24 x 2
12 x 4
16 x 3
Are the 5 expressions equivalent to 12 x 4
formulas A=bh/2 A=bh and I have 6in 4in 6in 10in and I have to find the area
Answer:
Lots of "ifs" here.
A=bh/2 is the formula for the area of a triangle.
A=bh is the formula for the area of a rectangle or a parallelogram.
If the 6 & 4 area the base & height of a rectangle, then (6)(4) = 24 in^2
If the 6 & 10 are the base and height of a triangle, then 1/2(6)(10) = 30 in^2
Step-by-step explanation:
For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exercise at a gym regularly. The college student records the number of minutes each person exercises in a given week. The college student believes that the mean number of minutes per week is lower for men than for women. The college student conducts a hypothesis test at the 5% significance level. The following is the output for the test: Two Sample T-Test Sample N Mean StDev SE Mean Men 75 60.75291 13.8806 1.602793 Women 68 64.76217 9.568889 1.160398 t-value = -1.9909, p-value = 0.02421, DF = 141 95 percent confidence interval upper bound for difference: -0.6750134 What conclusion can you draw from the output? a. The data provide sufficient evidence to reject the null hypothesis and to conclude that the mean number of minutes exercised per week is lower for men than for women. b. We accept the null hypothesis, and conclude that there is a difference in the mean number of minutes exercised per week for men and women. c. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is lower for men than for women. d. The data provide sufficient evidence to conclude that there is no difference in the mean number of minutes exercised per week for men and women.
Based on the provided output, the conclusion that can be drawn is that the data provide sufficient evidence to reject the null hypothesis and conclude that the mean number of minutes exercised per week is lower for men than for women.
In hypothesis testing, the null hypothesis assumes that there is no difference between the mean number of minutes exercised per week for men and women. The alternative hypothesis, in this case, is that the mean number of minutes per week is lower for men.
The t-value of -1.9909 and the associated p-value of 0.02421 indicate that the test statistic falls in the critical region at the 5% significance level. Since the p-value is less than the significance level, we reject the null hypothesis. This means that there is sufficient evidence to support the alternative hypothesis that the mean number of minutes exercised per week is lower for men than for women.
Furthermore, the 95 percent confidence interval upper bound for the difference in means (-0.6750134) being negative supports the conclusion that the mean number of minutes exercised per week is lower for men.
Therefore, the correct conclusion is option a: The data provide sufficient evidence to reject the null hypothesis and to conclude that the mean number of minutes exercised per week is lower for men than for women.
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can anyone solve this?
Answer:
3×0+1=1
Step-by-step explanation:
i hope that helps
#CarryonlearningState whether the following categorical propositions are of the form A, I, E, or O. Identify the subject class and the predicate class. (1) Some cats like turkey. (2) There are burglars coming in the window. (3) Everyone will be robbed.
Statement 1: Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey, statement 2: There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window and statement 3: Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.
The given categorical propositions and their forms are as follows:
(1) Some cats like turkey - Form: I:
Subject class: Cats,
Predicate class: Turkey
(2) There are burglars coming in the window - Form: E:
Subject class: Burglars,
Predicate class: Not coming in the window
(3) Everyone will be robbed - Form: A:
Subject class: Everyone,
Predicate class: Being robbed
In the first statement:
Some cats like turkey, the form is I, the subject class is Cats, and the predicate class is Turkey.
In the second statement:
There are burglars coming in the window, the form is E, the subject class is Burglars, and the predicate class is Not coming in the window.
In the third statement:
Everyone will be robbed, the form is A, the subject class is Everyone, and the predicate class is Being robbed.
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Simplify the expression.
Answer:
-10p/3+32-3/2^p
Step-by-step explanation:
an analyst believes that protein powder builds muscle mass while long-distance running reduces muscle mass. she collects data on subjects (pounds of muscle mass, ounces of protein powder, and hours of running) and runs a regression. what is the dependent variable?
The dependent variable is Muscle mass.
An analyst believes that protein powder builds muscle mass while long-distance running reduces muscle mass.
She collects data on subjects (pounds of muscle mass, ounces of protein powder, and hours of running) and runs a regression.
Given information,
We get that muscle mass depends positively on protein powder and muscle mass depends negatively on long-distance running.
This implies that Muscle mass is a dependent variable.
Therefore, The correct option is option B.
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Incomplete Question:
an analyst believes that protein powder builds muscle mass while long-distance running reduces muscle mass. she collects data on subjects (pounds of muscle mass, ounces of protein powder, and hours of running) and runs a regression. what is the dependent variable?
Intercept.Muscle mass.Protein powder.Running hours.when the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. what was the area of the original square garden?
the area of the original square garden is 80 square meters.
Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.
We want to find the area of the original square, so the value of a².
(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.
(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.
the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.
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Factor the expression completely.
18 x − 21 18x−21
Answer:
3( 6x-7)
Step-by-step explanation:
18 x − 21
Factor a 3 out of each term
3*6x - 3*7
3( 6x-7)
Answer:
Factor 18x−21
18x−21
=3(6x−7)
Answer:
3(6x−7)
Step-by-step explanation:
Which value or in the solution set of the inequality − 2/3 x + 13 ≥ − 1
Answer:
x\(\leq\)21
Step-by-step explanation:
(-2/3)x+13≥ -1
(-2/3)x≥ -14 (I subtracted by 13 on both sides)
x\(\leq\)-14*(-3/2) (I divided by -2/3 on both sides)
x\(\leq\)21
Which of the following graphs is described by the function given below?
y=-6x-7
10+
pu
20
-10
A. Graph A
OB. Graph B
OC. Graph C
OD. Graph D
10
The graph described by the function y = -6x - 7 is Graph B.
In what way does Graph B represent the function y = -6x - 7?The graph described by the function y = -6x - 7 is Graph B. Graph B represents the function by displaying a straight line with a slope of -6 and a y-intercept of -7. The negative slope indicates that the line slopes downward from left to right, while the y-intercept denotes the point where the line intersects the y-axis.
As x increases, y decreases at a rate of 6 units for every 1 unit increase in x. The line passes through the point (-1, 1) and extends infinitely in both directions. Graph B accurately reflects the behavior and characteristics of the given function y = -6x - 7.
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Complete the table to show the interest earned for different savings principals, interest rates, and time periods
The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.
Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)
$1,000 | 2% | 1 year | $20
$5,000 | 4% | 2 years | $400
$10,000 | 3.5% | 3 years | $1,050
$2,500 | 1.5% | 6 months | $18.75
$7,000 | 2.25% | 1.5 years | $236.25
To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.
For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.
For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.
For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.
For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.
For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.
These calculations show the interest earned for different savings principals, interest rates, and time periods.
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Suppose the cost of an item is c. First, the cost is discounted by 30%. Then sales tax of 6.5% is added to the sales price. Write an algebraic expression for the final cost of the item using the variable c.
The Algebraic expression for the final cost of the item using the variable c is 0.7455c
The cost of the item is c
Algebraic expression after discounting the cost by 30%
c - 30%of c
c- 0.3c
0.7c
Now, Algebraic expression after the application of 6.5% of sales tax
0.7c + 6.5%of 0.7c
0.7c +0.065(.7c)
0.7c +0.0455c
0.74.55c
Hence, 0.7455c is the algebraic expression for the final cost of the item using the variable c.
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
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Mila and Nadia have R480 between them.
Mila has 7 times as much as Nadia.
How much does each of them have?
Answer:
Mila= 420 Nadia= 60
Step-by-step explanation:
Let's call Mila 7x. And x to Nadia. The two of them had a total of 480s.
Then we say 7x + x. Their total is 8x. So 480 = 8x. We divide both sides by 8. Here x = 60. Since Mila is 7x, we find Mila as 7.60 = 420, and since Nadia as x, we find Nadia as 1.60 = 60.
If there is any place you don't understand, you can ask.
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