Vocabulary How is a constant term different from a variable term for an expression that represents a real-world situation? Drag the term to complete each sentence. constant term variable term A changes in value whenever the value of the variable changes. А) does not change.​

Answer:

x-intercepts: (-6,0) and (2,0)

y-intercepts: (0,-12)

Minimum value at x = -2

The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

Joint variation describes a situation in which, while the other variables are held constant, the value of one variable relies on the values of two or more additional variables.

Joint variation is used to describe when more than two variables are directly correlated or when one variable changes as a result of the change product of more than two variables. X can be symbolically expressed as X YZ if it is in joint variation with Y and Z. If Y is also constant, then X and Z directly depend on one another.

Joint variation is a type of variation where a quantity changes when two or more other numbers are multiplied together. For instance, when a rectangle's length or breadth changes, so does its area. Where A is the area, l is the length, and w is the width, we say that A = lw.

Joint Variation of x,y and z

z = kxy

k is the cofficient

for x = 7, y = 3 and z = -14

-14 = k*3*7

⇒k = -2/3

for x= 3 and z = -8

-8 = (-2/3)*3*y

y = 4

The equation is z = (-2/3)*xy with of x , y and z are jointly varied.

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The pounds of apples that he get if he goes to David’s orchard is 20 pounds.

Let the assumed amount with him be $40.

It should be noted that for David's orchard, the first ten pounds are $2 per round and each additional round is $1 per pound.

Therefore, the expression to illustrate this will be:

($2 × 10) + ($1 × r)

where r = additional pounds

Therefore,

($2 × 10) + ($1 × r) = $40

20 + r = 40

r = 40 - 20

r = 20

He will get 20 pounds.

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I'll do problem 6 to get you started

x = number of people training all 3 sports.

This is because all 3 sports are needed for the triathlon

There are 35 swimmers total. 9 of which are also cyclers (but not runners), and there are 13 swimmers who are also runners (but not cyclers)

That leaves 35-9-13-x people who are swimmers only. I'll leave this expression un-simplified so you can see where the numbers are coming from. Take note of where I'm placing this in the venn diagram below.

There are 32 cyclers. Of this group, 9 are swimmers (but not runners) and 11 are runners (but not swimmers). That leaves 32-9-11-x people who are cyclers only.

There are 38 runners. Of this group, 13 are swimmers (but not cyclers) and 11 are cyclers (but not swimmers). That leaves 38-13-11-x people who are runners only.

All of these values are honestly hard to keep track of. This is why a visual approach using a Venn Diagram is recommended. See the diagram below.

The idea is that every value in the diagram then adds up to the 58 total attendees. This helps form the equation needed to solve for x.

Such an equation is possible because each attendee participates in at least one of the sports mentioned. No values will be outside of all three circles at the same time.

(35-9-13-x)+(32-9-11-x)+(38-13-11-x)+(9)+(13)+(x)+(11)=58

-2x+72 = 58

-2x = 58-72

-2x = -14

x = -14/(-2)

x = 7

Answer:

x = - 3, x = 0.5

Step-by-step explanation:

Given

10x² + 5x - 15 = - 12 + 8x² ( subtract 8x² from both sides )

2x² + 5x - 15 = - 12 ( add 12 to both sides )

2x² + 5x - 3 = 0 ← in standard form

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Answer:

Step-by-step explanation:

\(\text{Did you mean}\\ \\ \sqrt[3]{15-7}\\ \\ \sqrt[3]{8}=2\text{ which IS a rational number}\)

The population of interest is all students at her high school

The community or group that a researcher attempts to draw conclusions from is known as a population of interest. The surveyor is interested in learning additional information about a segment of the general population. Numerous research projects call for particular interest groups to make decisions in light of their findings.

When researching the opinions of students at her high school over the new school hours suggested by the school board, Kristen is interested in "all students at her high school." She wants to know what high school students think, and the only way to find out is to ask the students themselves. The other choices are incorrect because the study is focused on the opinions of the children at her school rather than theirs.

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The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

50 degrees

Step-by-step explanation:

just makes sense

Answer:

A and C

Step-by-step explanation:

The shapes that have 4 congruent sides are squares and rhombi.

A passenger can travel approximately 6.875 miles for $20.

An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "

We want to find the distance (in miles) that a passenger can travel for $20. Let's call this distance d.

Using the given function, we can set up an equation:

20 = 2.56d + 2.40

Solving for d:

2.56d = 20 - 2.40

2.56d = 17.60

d = 6.875

Therefore, a passenger can travel approximately 6.875 miles for $20.

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The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Method:

Front: 6x8 = 48/2 = 24

Back: Also 24

Base: 8x4 = 32

Left: 6x4=24

Add your answers:

24 + 24 + 24 + 32 + 40

Answer:

TSA is 144 cm²

Answer:

16 < 24 < 25

Step-by-step explanation:

√16 = 4

√25 = 5

Answer:

y^7

Step-by-step explanation:

We know that a^b / a^c = a^( b-c)

y^9/y^2

y^(9-2)

y^7

Answer:

Step-by-step explanation:

The rule for division when the bases are like is to subtract the exponents:

\(\frac{y^9}{y^2}=y^{9-2}=y^7\)

Answer:

True

Step-by-step explanation:

When two lines are parallel, the corresponding angles formed by the transversal (intersecting line) are congruent. This is called the corresponding angles postulate. It can be used in reverse: if two corresponding angles are congruent, then the non-transversal lines are parallel.

Answer:

Step-by-step explanation:

Angles 4 and 5 are corresponding; this means that they are sitting in the same places within their angle "bunch" for lack of a better word. We are then told that they are are congruent which means that they have the exact same measure. Corresponding angles can exist without being congruent, but because they are, that means that A and B HAVE to be parallel. So true.

The equation of the line in slope-intercept form is  \(y = (7/2)x + 6\).

The given line is \(2x + 7y = -1\).

Let's find the slope of this line.

\(2x + 7y = -1\)

The slope-intercept form is

\(y = mx + b\)

where m is the slope and b is the y-intercept.

\(2x + 7y = -17y\)

=\(-2x - 1y\)

= \((-2/7)x - 1/7\)

The slope of this line is -2/7. The line that is perpendicular to this line will have the negative reciprocal of the slope.The negative reciprocal of -2/7 is 7/2.

The equation of the line that passes through (-2,-1) and is perpendicular to

\(2x + 7y = -1\)

in slope-intercept form is

\(y = mx + b\),

where

m = 7/2,

x = -2

and y = -1.

Substitute these values into the formula and solve for b.

\(-1 = (7/2)(-2) + b-1\)

= \(-7 + bb = 6\)

The equation of the line in slope-intercept form is

\(y = (7/2)x + 6\).

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The given radical expression is (√x)^5. To rewrite it in rational exponent form, we need to express the square root (√) as a fractional exponent.

The square root (√) of x can be written as x^(1/2).

To raise x^(1/2) to the power of 5, we can multiply the exponents: (x^(1/2))^5 = x^(5/2).

Therefore, the radical expression (√x)^5 can be rewritten as x^(5/2) in rational exponent form.

In summary, (√x)^5 is equivalent to x^(5/2) in rational exponent form.

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Step-by-step explanation:

I solved it by steps...

I hope you understand...

-1/2

To find the slope of the line between two points, we use the equation (y2-y1)/(x2-x1)

Substitute the values given for the xs and ys:

(7-5)/(-1-3)

2/(-4)

simplify: -1/2

A. The Hardy-Weinberg Equilibrium equation is:

1 = p^2 + 2pq + q^2

- p: the frequency of the dominant allele (S)

- q: the frequency of the recessive allele (s)

- 1: represents the total possibilities or the sum of the allele frequencies

- p^2: the frequency of the homozygous dominant genotype (SS)

- 2pq: the frequency of the heterozygous genotype (Ss)

- q^2: the frequency of the homozygous recessive genotype (ss)

B. After one generation of selection, the frequencies of S and s (p' and q') are as follows:

p' = p^2 + 0.5*(2pq) = 0.49 + 0.21 = 0.70

q' = q^2 + 0.5*(2pq) = 0.09 + 0.21 = 0.30

In this case, after one generation, the frequency of the dominant allele (S) remains the same at 0.70, while the frequency of the recessive allele (s) also remains the same at 0.30.

C. If selection were to operate in the same way for many generations, the eventual frequency of the recessive allele (s) would remain 0.30 based on the Hardy-Weinberg Equilibrium.

D. Taking into account that heterozygotes (Ss) have resistance to malaria and higher reproductive success, and SS individuals have reduced reproductive success, the frequencies of S and s after one generation of selection can be calculated as follows:

p' = 0.6(p^2) + 2pq + 0.9(q^2) = 0.6(0.49) + 0.21 + 0.9(0.09) = 0.585

q' = 0.4(p^2) + 2pq + 0.1(q^2) = 0.4(0.49) + 0.21 + 0.1(0.09) = 0.415

After one generation of selection under the new selective regime, the frequency of the dominant allele (S) is 0.585, and the frequency of the recessive allele (s) is 0.415.

E. Yes, the answer to question IC would change under this new selective regime because natural selection can affect the frequency of alleles. The selection against SS homozygotes and the advantages of heterozygotes (Ss) result in changes in the allele frequencies.

F. Sickle-cell anemia is expected to be more common in West Africa compared to Siberia. This is because malaria is a tropical disease transmitted by tropical mosquitoes, and in West Africa, where malaria is common, the heterozygotes (Ss) have higher reproductive success due to their resistance to malaria.

As a result, the frequency of the recessive allele (s) remains relatively high due to the selective advantage it provides against malaria. In Siberia, where malaria is not prevalent, there would be less selective pressure favoring the sickle cell allele.

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Answer:

7% of 33= 2.1

2% of 640= 12.8

15% of 470=70.5

7/9 of 51= 119/3

.52 of 62= 32.24

Answer:

1) 2.31

2) 12.8

3) 72

4) 44.625

5) 32.24

Step-by-step explanation:

7% of a number is simply 0.07*the number.

7/8 is just .875*the number

Hope it helps <3

A conditional statement (also called an If-Then Statement) is a statement with a hypothesis followed by a conclusion. ... The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.

Answer:

4x - 4

Step-by-step explanation:

4 × x = 4x

4 × -1 = -4

4x - 4

Answer:

4x-4

Step-by-step explanation:

\(\boxed{\sf sin\theta=\dfrac{P}{H}}\)

\(\\ \sf\longmapsto sin\theta=\dfrac{38}{53}\)

\(\\ \sf\longmapsto sin\theta=0.7\)

\(\\ \sf\longmapsto sin\theta=\dfrac{1}{1.4}\)

\(\\ \sf\longmapsto sin\theta=\dfrac{1}{\sqrt{2}}\)

\(\\ \sf\longmapsto sin\theta=sin45°\)

\(\\ \sf\longmapsto \theta=45°\)

Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

area triangle:

(1.7m×2m)×2

= 1.7m²

-> 2 triangles so: 1.7m²×2= 3.4m²

area rectangles(walls):

2m×3m

= 6m²

-> 2 walls so: 6m²×2=12m²

area bottom rectangle:

3m×2m=6m²

-> total area:

6m²+12m²+3.4m²= 21.4m²

The probability of the 6th order being the order with the free appetizer is 0.0417 (approx).

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

The probability of getting a free appetizer is 1/18.

The probability of not getting a free appetizer is 17/18.

If the restaurant gives away an appetizer on the 6th order, then there must have been 5 orders before the 6th one that had no free appetizer, followed by the one with the free appetizer.

\(P (X = 6) = P(N N N N N F)\)

= 17/18 x 17/18 x 17/18 x 17/18 x 17/18 x 1/18

\(= \frac{17^4}{18^5}\)  ≈ 0.0417

Thus, the probability of the 6th order being the order with the free appetizer is 0.0417 (approx).

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The histogram represents the sampling distribution of the proportion of heads in 10 flips of the coin, which is an example of a binomial distribution.

In this scenario, the parameter of interest is the true population proportion of heads in a coin flip. The process of flipping the coin 10 times and recording the proportion of heads is an example of a binomial distribution, where each flip is a Bernoulli trial with a probability of success (getting heads) of 0.5.
By repeating this process many times and creating a histogram of the results, we are creating a sampling distribution of the proportion of heads in 10 flips of the coin. This allows us to see the variability of the proportion of heads we could get from different samples of the same size.
If we are using simple random sampling, meaning each possible sample of 10 coin flips has an equal chance of being chosen, then there should be no bias present in our results. However, if we are using a different sampling method, such as convenience sampling, there could be a bias present in our results.

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