We have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are [tex](-2, -3)[/tex] and [tex](1, 0)[/tex].
What is a System οf Equatiοns?A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.
While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.
Tο prοve that these cοοrdinate pοints are sοlutiοns, we need tο substitute them intο bοth equatiοns and verify that they satisfy the equatiοns. Let's start with (-2, -3):
[tex]F(-2) = (-2)^2 + 2(-2) - 1 = 4 - 4 - 1 = -1[/tex]
[tex]g(-2) = (-2) - 1 = -3[/tex]
We can see that [tex]F(-2) = g(-2)[/tex] , sο[tex](-2, -3)[/tex]is a sοlutiοn.
Nοw let's check (1, 0):
[tex]F(1) = 1^2 + 2(1) - 1 = 2[/tex]
[tex]g(1) = 1 - 1 = 0[/tex]
Again, we can see that F(1) = g(1), sο (1, 0) is alsο a sοlutiοn.
Therefοre, we have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are (-2, -3) and (1, 0).
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A creative writing competition accepts only
poems and stories.
In one year, the competition received 1000
entries.
750 of the entries were poems.
24% of the poems and 65 of the stories were
shortlisted for a prize.
a) Draw a frequency tree to show the
information above.
b) An entry is picked at random. What is the
probability that it is a poem that has not been
shortlisted?
Give your answer as a decimal.
c) A story is picked at random. What is the
probability that it has not been shortlisted?
Give your answer as a decimal.
Answer:
b) 0.57
c) 0.74
Step-by-step explanation:
part a:
frequency graph is attached with this answer (in png format).
part b:
let A be the event an entry is picked at random and the entry is a poem that has not been shortlisted.
P(A) = [tex]\dfrac{\text{number of poems not shortlisted}}{\text{total number of entries}}[/tex]
P(A) = [tex]\dfrac{570}{1000}[/tex] (see the frequency graph)
P(A) = 0.57
part c:
let B be the event a story is picked at random and the story has not been shortlisted.
P(B) = [tex]\dfrac{\text{number of stories not shortlisted}}{\text{total number of stories}}[/tex]
P(B) = [tex]\dfrac{185}{250}[/tex] (see the frequency graph)
P(B) = 0.74
Hopefully this answer helped you!!
Zain is using a protractor to measure an angle.
What is the measure of the angle?
The measure of the angle that Zane is using the protractor is a 113 degrees.
Degree is the unit of measure of an angle and is measured by using the geometric tool - a protractor. A degree is denoted by the symbol '°'. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts.
Therefore, The measure of the angle that Zane is using the protractor is a 113 degrees.
Find the length of BC with work
Answer:
Step-by-step explanation:
add c with b and then add a multiply 30 and divide by 12
if a destination goal is created for a newsletter sign-up and a user completes the newsletter sign-up three times in three separate sessions, how many goal conversions will analytics count?3621
Analytics will count three goal conversions if a user completes the newsletter sign-up three times in three separate sessions.
When a goal is set up in analytics, it is assigned a unique ID. When a user completes the desired action that triggers the goal, the ID is recorded in the user's session data. Each time the user completes the action, a new session is created, and a new goal completion is recorded with a unique ID.
Therefore, if the user completes the newsletter sign-up three times in three separate sessions, analytics will count three goal conversions, each with a unique ID.
It's worth noting that while this behavior is typical for most analytics platforms, it's possible to configure goals in different ways, so the behavior may vary depending on the specific implementation. Therefore, it's important to consult the analytics documentation or work with a knowledgeable analyst to confirm the expected behavior.
Therefore, the correct answer is three goal conversions will be counted in analytics.
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the trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)
Answer:
24.3ft
Step-by-step explanation:
36.2ft - 15ft = 21.2ft
Cade height = 6.2 - 2.5 = 3.7
21.2 + 3.7 = 24.9ft
24.9ft - 15.6ft = 24.3ft
A poker hand consists of 5 cards from a standard deck of 52. How many hands will include all red cards or all black cards?
Answer:There are two cases to consider: a hand that consists of all red cards and a hand that consists of all black cards.
Case 1: All red cards
There are 26 red cards in a standard deck of 52 cards. To form a 5-card hand consisting of all red cards, we need to choose 5 cards from the 26 red cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Case 2: All black cards
Similar to the first case, there are 26 black cards in a standard deck of 52 cards. To form a 5-card hand consisting of all black cards, we need to choose 5 cards from the 26 black cards. The number of ways to do this is:
C(26, 5) = (26!)/(5!21!) = 65,780
Therefore, the total number of hands that include all red cards or all black cards is the sum of the two cases:
65,780 + 65,780 = 131,560
So there are 131,560 hands that consist of either all red cards or all black cards.
Step-by-step explanation:
I need somebodys help quickly please!
(look at the attachment it shows the math equation).
Answer:
First box is seven; second box is 16; third box is 14
Step-by-step explanation:
Since a square has all equal sides, we know that s+s+s+s or 4s=Perimeter.
SInce we are finding the area of a square, the equation would be s^2. 7 squared is 49, 16 squared is 256, and 14 squared is 196.
The correlation coefficient is always a number between ____ and ___.
A correlation coefficient is consistently a number between 1 and - 1 .
The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).
The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.
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8x=-10y slope and y intercept
Answer:
To solve the equation 8x = -10y for the slope and y-intercept, we need to first rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can divide both sides of the equation by -10, which gives us:
y = (-8/10)x
Simplifying further, we get:
y = (-4/5)x
Therefore, the slope of the line represented by this equation is -4/5. This means that for every increase of 1 in x, y decreases by 4/5.
To find the y-intercept, we can set x to 0 and solve for y:
y = (-4/5)(0)
y = 0
Thus, the y-intercept is 0.
In summary, the slope of the line represented by 8x = -10y is -4/5 and its y-intercept is 0.
Step-by-step explanation:
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Answer: x=5y/4
Step-by-step explanation:
8x=10y
Divide both sides by 8
8x/8 = 10y/8
8x divided by 8, will cancel out resulting in x.
So, your final answer will be x=5y/4
Triangle RST was dilated by a scale factor of 3 to create triangle LMN. What is true about the special relationship between the trigonometric ratios of the two triangles? Choose ALL that apply.
A.
sin angle R = ST/RT
B.
sin angle L = 3(ST)/3(RT)
C.
sin angle R = 3(MN)/3(LM)
D.
sin angle L= MN/NL
The answers are sin angle R = ST/RT and sin angle L = 3(ST)/3(RT) Fοr the given questiοn trigοnοmetry.
Thus option A & B are correct.
What is trigοnοmetric ratiοs?Trigοnοmetric ratiοs are mathematical relatiοnships between the sides and angles οf a right triangle. The three main trigοnοmetric ratiοs are sine, cοsine, and tangent, abbreviated as sin, cοs, and tan.
The sine οf an angle is the ratiο οf the length οf the side οppοsite the angle tο the length οf the hypοtenuse. The cοsine οf an angle is the ratiο οf the length οf the adjacent side tο the length οf the hypοtenuse. The tangent οf an angle is the ratiο οf the length οf the οppοsite side tο the length οf the adjacent side. These ratiοs are useful in sοlving prοblems invοlving right triangles and have many applicatiοns in fields such as physics, engineering, and navigatiοn.
We knοw that when a triangle is dilated by a scale factοr οf k, all cοrrespοnding sides are multiplied by k, and all cοrrespοnding angles remain cοngruent.
Using this fact, we can determine the relatiοnships between the trigοnοmetric ratiοs οf the twο triangles:
A. Sin angle R = ST/RT is true fοr bοth triangles, as the sine οf an angle is defined as the ratiο οf the οppοsite side tο the hypοtenuse, which dοes nοt change when dilated.
B. Sin angle L = 3(ST)/3(RT)simplifies tο Sin angle L = ST/RT, which is true fοr bοth triangles (as shοwn in part A).
C. Sin angle R = 3(MN)/3(LM) simplifies tο sin angle R = MN/LM, which is nοt necessarily true. This is because the cοrrespοnding sides οf the triangles are nοt prοpοrtiοnal tο each οther.
D. Sin angle L = MN/NL is nοt necessarily true fοr the same reasοn as in part C.
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A submarine dives 240 meters below the surface of the water and then rises 65 meters.
Which integer describes the position of the submarine in relation to the surface of the
water?
A. -305 m
B. -175 m
C.175 m
D 305 m
Answer:
B
Step-by-step explanation:
-240 +65 = -175
(We use a -240 instead of 240 because it's below water.) :)
What is the surface area of this composite figure? The slant height of the cone is 3. The height of the cone is approximately 1.658. (It is all one figure. Watch for surfaces that are not needed in your formulas because they are not actually surfaces in this figure.)
150л units²
125л units³
100л units²
Answer:
125pi units cubed
Step-by-step explanation:
A roll of copper tubing is 50 ft. long. If gas range connectors must be 30 in. long, how many connectors can be cut from the roll of tubing? (Ignore cutting waste.)
Does the long division process end or does it continue indefinitely?
Answer:
It depends, sometimes it continues with a pattern in the decimal places, sometimes it ends.
Step-by-step explanation:
Please solve this equation
24+0. 44x=19+1. 69x
Given equation is: 24+ 0.44x = 19+ 1. 69x is x = 4.
Equation:
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values of the variable. A conditional comparison is only true for certain values of a variable.
According to the Question:
Given equation:
24+0. 44x = 19+ 1. 69x
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
24 - 19 = 1.69x - 0.44x
⇒ 5 = 1.25x
⇒ x = 5/1.25
⇒ x = 4
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Plssssss helppp
What do you think an appropriate domain for the mold area function A is? Explain your
reasoning
Assuming that the function A calculates the surface area of a mold, the appropriate domain for A would be a set of all possible molds, which can be represented by a set of positive real numbers.
It is important to note that the mold's geometry, size, and complexity will affect the calculation of its surface area. Therefore, the domain of the mold area function A should include all possible variations of mold shapes and sizes.
In practical applications, the domain of A may also be limited by the manufacturing capabilities or constraints, such as the maximum size or complexity of molds that can be produced. In such cases, the domain of A may need to be further restricted to reflect these limitations.
Overall, the appropriate domain for the mold area function A would depend on the specific context and application of the function.
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A student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday. What is the percent decrease in homework time from Monday to Tuesday?
If a student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday, then there was a 40% decrease in homework time from Monday to Tuesday.
To calculate the percent decrease in homework time from Monday to Tuesday, we need to find the difference between the two values and then divide that difference by the original value (Monday’s homework time). The difference between 50 minutes and 30 minutes is 20 minutes. Dividing this difference by the original value (50 minutes) gives us:
(20 / 50) x 100% = 40%
Therefore, there was a 40% decrease in homework time from Monday to Tuesday.
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The figure below is dilated by a factor of 1/4 centered at the origin. Plot the resulting image.
Check the picture below.
multiply the y-value of each point by 1/2 and drag the blue point to its new location.
The function y = ∛x when transformed is added as an attachment
Transforming the functionFrom the question, we have the following parameters that can be used in our computation:
y = ∛x
When the y values are multiplied by 1/2 the rule is
(x, 1/2y)
To transform the function y = ∛x by the point (x, 1/2y), we can use the following steps:
Replace y with 1/2y in the original function: y = ∛x becomes 1/2y = ∛xSolve for y: multiply both sides by 2 to get y = 2∛xTherefore, the transformation by the point (x, 1/2y) is y = 2∛x
See attachment for the graph
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we want to test if more than 6% of byu students are from texas. is the sampling distribution of p-hat approximately normal in this example? group of answer choices yes, because n > 30. no, because the sample distribution is not normal. no, because the sampling distribution of p-hat does not have a shape. yes, because np0 > 10 and n(1-p0) > 10.
Yes, because[tex]np0 > 10[/tex]and [tex]n(1-p0) > 10[/tex].
Thus, the sampling distribution of p-hat is approximately normal, given the conditions of [tex]np0 > 10 and n(1-p0) > 10.[/tex]
This is because the sampling distribution of p-hat follows the Central Limit Theorem, which states that when sample sizes are greater than 30,
the sampling distribution of the sample proportion will be approximately normal. The Central Limit Theorem is used in this example because the number of BYU students from Texas (n) is greater than 30, so the sample proportion (p-hat) is normally distributed.
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Please helppp
To keep some privacy about the students, a professor releases only summary
statistics about student scores on a difficult quiz.ctice problems
mean standard deviation minimum Q1
66.91
12.74
12
57
median
66
Q3 maximum
76
100
Based on this information, what can you know about outliers in the student scores?
A. There is an outlier at the upper end of the data.
B. There is an outlier at the lower end of the data.
C. There are outliers on both ends of the data.
D. There is not enough information to determine whether there are any outliers.
Answer:
B
Step-by-step explanation:
How do the sulotions of the two inequalities differ are any sulotions the same x+5<8 and x+5>8 B x+5_< 8 and x+5_>8
Solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.
The two inequalities are: x + 5 < 8 and x + 5 > 8. The first inequality states that the sum of x and 5 is less than 8, while the second inequality states that the sum of x and 5 is greater than 8.
To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x < 3. This means that any value of x that is less than 3 will satisfy the inequality.
To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x > 3. This means that any value of x that is greater than 3 will satisfy the inequality.
The solutions of the two inequalities differ in terms of the values of x that satisfy each inequality. The first inequality has a solution set that consists of all values of x less than 3, while the second inequality has a solution set that consists of all values of x greater than 3. Therefore, the solutions of the two inequalities do not overlap.
The second set of inequalities are x + 5 ≤ 8 and x + 5 ≥ 8. The first inequality states that the sum of x and 5 is less than or equal to 8, while the second inequality states that the sum of x and 5 is greater than or equal to 8.
To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≤ 3. This means that any value of x that is less than or equal to 3 will satisfy the inequality.
To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≥ 3. This means that any value of x that is greater than or equal to 3 will satisfy the inequality.
The solutions of the two inequalities in this case do overlap. The common solution is x = 3, which satisfies both inequalities since it is both less than or equal to 8 and greater than or equal to 8. Therefore, the solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.
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Evaluating functions
Linear and quadratic or cubic
Answer:
f(3) = -39g(-6) = -28Step-by-step explanation:
You want f(3) and g(-6) when f(x) = -4x² -3 and g(x) = 5x +2.
Function evaluationTo find the value of the function for a particular value of the variable, put that value in place of the variable and do the arithmetic.
f(3) = -4(3²) -3 = -4(9) -3 = -36 -3
f(3) = -39
g(-6) = 5(-6) +2 = -30 +2
g(-6) = -28
__
Additional comment
Your calculator can help with the arithmetic.
What are the perimeter and area of triangle XYZ ?
Answer:
B) P = 42; A = 84
Step-by-step explanation:
Perimeter:
You have two right triangles, so you need to find the third side length.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]c^{2}[/tex]
25 + 144 = [tex]c^{2}[/tex]
169 = [tex]c^{2}[/tex]
[tex]\sqrt{169}[/tex] = [tex]\sqrt{c^{2} }[/tex]
13 = c
The top right missing outside length is 13
We do the same thing to find the missing bottom outside.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]12^{2}[/tex] + [tex]9^{2}[/tex] = [tex]c^{2}[/tex]
144 + 81 = [tex]c^{2}[/tex]
225 = [tex]c^{2}[/tex]
[tex]\sqrt{225}[/tex] = [tex]\sqrt{c^{2} }[/tex]
15 = c
The perimeter of triangle xyz is 5 + 9 + 13 + 15 = 42 units
Area:
a = 1/2 bh
a= 1/2 (5 + 9) (12)
a = 1/2 (14)(12)
a = 84 [tex]units^{2}[/tex]
Helping in the name of Jesus.
In DEF, f= 960 inches, m/D=101° and mZE=27°. Find the length of e, to the
nearest 10th of an inch.
The length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
We shall first evaluate for the angle m∠F and then solve for the e using the sine rule as follows:
m∠F = 180° - (27 + 101) {sum of interior angles of a triangle}
m∠F = 52°
e/sin27 = 960/sin52
e = (960 × sin27)/sin52 {cross multiplication}
e = 553.0773
Therefore, the length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.
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The results of a survey show that the percent of adults in a certain town who want to change the name of the town is in the interval [0.38,0.41].
The point estimate for the percent who want to change the name of the town is 39.5%.
The poll's margin of error is 1. 5 %.
The town most likely will not change its name because the point estimate is less than half.
How to find the point estimate ?The point estimate for the percent who want to change the town's name is the midpoint of the interval [0.38, 0.41]. To find the midpoint, add the endpoints of the interval and divide by 2:
(0.38 + 0.41) / 2 = 0.79 / 2 = 0.395
So, the point estimate is 39.5%.
The margin of error is half the width of the interval. To find the width, subtract the lower endpoint from the upper endpoint and divide by 2:
(0.41 - 0.38) / 2 = 0.03 / 2 = 0.015
So, the margin of error is 1.5%.
Based on the given data, the town is most likely not going to change its name. The point estimate, 39.5%, is less than 50%, which indicates that less than half of the surveyed adults want to change the town's name. The margin of error (1.5%) is relatively small compared to the point estimate, which means that the true percentage is likely to be within 1.5% of the point estimate.
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how do you do this question, I can't seem to get the answer
Answer:
74π cm²
Step-by-step explanation:
You want to know the painted area of a cone 10 cm in diameter and 12 cm high that has an unpainted hole in the base that has a 4 cm radius.
Lateral areaThe area of the curved surface of the cone is found using the given formula. To use that formula, we need to know the slant height of the cone. The slant height is the hypotenuse of a right triangle that is 12 cm high and has a base of 5 cm:
l² = r² +h²
l = √(5² +12²) = √(25 +144) = √169
l = 13 . . . . cm
Then the lateral area is ...
LA = πrl = π(5 cm)(13 cm) = 65π cm²
Base areaThe painted area of the base is the difference between the areas of circles 5 cm in radius and 4 cm in radius:
A = π(r₁² - r₂²) = π((5 cm)² -(4 cm)²) = π(25 -16) cm² = 9π cm²
Total painted areaThe painted area is the sum of the areas of the curved surface and the donut base:
A = 65π cm² +9π cm² = 74π cm²
__
Additional comment
The radius of the base is half the diameter. If you slice the cone through its vertex and perpendicular to its base, the cross section is an isosceles triangle with height 12 cm and base 10 cm. The altitude of that triangle divides it into two congruent right triangles that have base 5 cm and height 12 cm.
You may recognize this as the {5, 12, 13} right triangle, which tells you the slant height is 13 cm. If not, you can use the Pythagorean theorem to find the slant height, as above.
A fish-tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. Find the volume of the fish tank.
The volume of the fish tank is 2000 cubic centimeters, which is calculated by multiplying the length, width, and depth of the tank (25 x 10 x 8 = 2000).
The volume of a fish tank is an important piece of information to know when setting up a fish tank. To calculate the volume of a fish tank, you must multiply the length, width, and depth of the tank. In this example, the fish tank has a length of 25 centimeters, a width of 10 centimeters, and a depth of 8 centimeters. To calculate the volume of the fish tank, we would multiply these three measurements, 25 x 10 x 8 = 2000. This means that the fish tank has a volume of 2000 cubic centimeters. Knowing the volume of the fish tank is important for selecting the right type and size of filter, heater, and other equipment for the tank, as well as for selecting the right number and size of fish for the tank. Furthermore, it is necessary to know the volume of the tank when adding water and testing water parameters, such as pH and nitrate levels, as these readings are related to the size of the tank. Knowing the volume of a fish tank is essential for successful fish keeping.
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Students in ms seiko's made a line plot of the number of books they read over the summer what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order
The two numbers of books read that occur the least frequently are 7 and 15.
To determine which two numbers occur the least frequently, we need to count the number of tally marks for each number on the line plot. Based on the line plot, we can see that the number of tally marks for each number is as follows:
7: 1 tally mark
8: 2 tally marks
9: 3 tally marks
10: 4 tally marks
11: 2 tally marks
12: 4 tally marks
13: 3 tally marks
14: 2 tally marks
15: 1 tally mark
The two numbers that occur the least frequently are 7 and 15, as they each have only one tally mark.
Therefore, the answers to the question are: 7 in the first box and 15 in the second box.
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Students in ms seiko's made a line plot of the number of books they read over the summer.
books read
7 8 9 10 11 12 13 14 15
what two numbers of books read occur the least frequently enter your answers in the boxes in increasing order?
Adam calculates his annual salary (base pay and commission), y, using the model y = 0.28x + 38,000, where x represents his total sales for the year. What is the meaning of the y-intercept in the model?
A. The y-intercept represents Adam's base pay
B. The y-intercept represents the highest salary Adam can earn
C. The y-intercept represents Adam's total sales when he earned no commission
D. The y-intercept represents Adam's commission pay when he had zero total sales
the y-intercept represents Adam's commission pay when he had zero total sales
Answer: A
Step-by-step explanation:
The Y intercept is his base pay, because no matter what he is getting 38,000. So, his total salary will always start out at 38,000 then continue up with commission sales.