When Poll Pasked students to identify their favorite kind
of TV show, 12 students, 30% of the group, said their
favorite was Sports. Poll Q asked 3 times as many
students as Poll P.
G
How many students took Poll Q?

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Answer: A. (-1, -6)

Step-by-step explanation:

Use the midpoint formula:

[tex]midpoint = (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}) \\\\(6, -4) = (\frac{13+x_{2}}{2}, \frac{-2+y_{2}}{2})\\\\\frac{13+x_{2}}{2} =6\\\\13+x_{2}=6*2\\\\x_{2}=12-13=-1\\\\ \\ \frac{-2+y_{2}}{2}=-4\\\\-2+y_{2}=(-4)*2\\\\y_{2}=-8+2=-6\\\\\\\left \{ {{x_{2}=-1} \atop {y_{2}=-6}} \right.[/tex]

Answer:

3/ 7

Step-by-step explanation:

We know that it is an even ball

2,4,6,8,10,12,14 are even balls

2,4,6,8 are red and 10,12,14 are white

P ( white) = white even / total even

              = 3/ 7

It looks like the equation is

[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]

Right away, we notice that any solution to this equation must be positive, so x > 0.

For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to

[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that

[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]

[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]

Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that

[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]

For x ≠ 0, we have [tex]\frac xx=1[/tex], so that

[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]

Take the antilogarithm of both sides:

[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]

[tex]\dfrac{2x}5 = 30[/tex]

Solve for x :

[tex]2x = 150[/tex]

[tex]\boxed{x=75}[/tex]

Step-by-step explanation:

I think something went wrong with the answer options you provided. and maybe with the problem statement itself.

I see 3 function definitions.

I can tell you what they are and use the provided option phrasing as closely as possible :

h(x) = 0 is a horizontal line (in fact the x-axis)

k(x) = 4x² + 312 is a parabola with the opening upwards

f(x) = x - 1 is a line with positive slope (going from left to right the line goes up)

Answer:

[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]

Step-by-step explanation:

One is given the following equation, and the problem asks one to identify the rational roots of the equation:

[tex]x^4-3x^2+6=0[/tex]

The rational root theorem states that the list of positive and negative factors of the constant term over the factors of the coefficients of the term to the highest degree will yield a list of the rational roots of the equation. Use this theorem to generate a list of all possible ration roots of the equation.

[tex](+-)\frac{6,3,2,1}{1}[/tex]

Now rewrite this list in a numerical format:

[tex]6, -6, 3, -3, 2, -2, 1, -1[/tex]

This is the list of the possible rational roots. One has to synthetically divide each of these numbers by the given polynomial equation to find the actual rational roots. However, the problem only asks for the possible rational roots, not the actual rational roots, thus, this is not included.

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on

Answer:

-243

Step-by-step explanation:

(-3) (-3) (-3) (-3) (-3) = - 243

[tex]\frac{1}{-243 }[/tex]

Answer:

Survey

Step-by-step explanation:

During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.

eueuhhbee×€×&÷;#;;#

shehdjdjjrnsns

shehehensndneee

nejeje

Answer:

it's 91.027%

Step-by-step explanation:

I hope i helped

Answer:

28

Step-by-step explanation:

78

Answer:

quneotentendeiporoqenouteetendxdin

Step-by-step explanation:

The shapes are the same size. Match the sides.

3x -1 = 17

Add 1 to both sides:

3x = 18

Divide both sides by 3:

X = 6

2y = 16

Divide both sides by 2

Y = 8

Answer: x = 6, y = 8

Answer:

0.054

Step-by-step explanation:

9 3/5% as a decimal is 0.054 (already to 3 decimal places)

Answer from Gauthmath

9 are just, well..., 9

3/5 are 0.6

because 1/5 is 0.2

so it's 9.6%, not so complicated I guess

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Answer:

f(x) is compressed horizontally

Step-by-step explanation:

Given

[tex]f(x) = \log(4x)[/tex]

[tex]g(x) = f(13x)[/tex]

Required

The effect on f(x)

[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.

So, we have:

[tex]f(13) = \log(4 * 13x)[/tex]

[tex]f(13) = \log(52x)[/tex]

So:

[tex]g(13) = \log(52x)[/tex]

Answer:

3 students

Step-by-step explanation:

since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.

7+5+10+x=25

x=25-22

=3

I hope this helps

Answer:

Answered March 20, 2021

This is a right angle triangle where the hypotenuse a^2 = b^2 + c^2

= 15^2 + 8^2 = 225+64= 289

289= 17^2

17 = hypotenuse

The sine of an angle is the ratio of the shortest side to the hypotenuse

= 8/17= 0.4705

sine^-1 0.4705 = 28°

Answer:

6

Step-by-step explanation:

You have 2 conditions.

1. The digits must be different.

2. The digits must add to 7.

There aren't very many

124

142

214

241

412

421

That's it. That's your answer. There are 6 of them

Given:

The function is:

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

To find:

The graph of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

It can be written as:

[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]

[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]

[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]

Putting [tex]x=0[/tex] to find the y-intercept.

[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]

[tex]f(0)=\dfrac{-5}{3}[/tex]

So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].

Putting [tex]f(x)=0[/tex] to find the x-intercept.

[tex]0=\dfrac{-2x-5}{x+3}[/tex]

[tex]0=-2x-5[/tex]

[tex]2x=-5[/tex]

[tex]x=\dfrac{-5}{2}[/tex]

[tex]x=-2.5[/tex]

So, the x-intercept is [tex]-2.5[/tex].

For vertical asymptote, equate the denominator and 0.

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

So, the vertical asymptote is [tex]x=-3[/tex].

The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.

[tex]y=\dfrac{-2}{1}[/tex]

[tex]y=-2[/tex]

So, the horizontal asymptote is [tex]y=-2[/tex].

End behavior of the given function:

[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]

[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]

Using all these key features, draw the graph of given function as shown below.

Answer:

The Answer Is A.

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.

Answer:

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

Step-by-step explanation:

2              3x

--------   - ----------

X^2-9    x^2 -5x+6

Factor

2                 3x

--------   -      ----------

(x-3)(x+3)   (x-3)(x-2)

Get a common denominator

2  (x-2)               3x(x+3)

--------   -             ----------

(x-3)(x+3)(x-2)   (x-3)(x-2)(x+3)

2x-4  - (3x^2 -9x)

-------------------------------

(x-3)(x-2)(x+3)

Distribute

2x-4  - 3x^2 +9x

-------------------------------

(x-3)(x-2)(x+3)

Combine like terms

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

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Answer:

329 miles

Step-by-step explanation:

Create a proportion where x is the distance the car can travel on 14 gallons of gas:

[tex]\frac{70.5}{3}[/tex] = [tex]\frac{x}{14}[/tex]

Cross multiply and solve for x:

3x = 987

x = 329

So, the car can travel 329 miles on 14 gallons of gas

Answer:

329 miles

Step-by-step explanation:

We can write a ratio to solve

70.5 miles      x miles

--------------- = ------------

3 gallons          14 gallons

Using cross products

70.5 * 14 = 3x

987=3x

Divide each side by 3

987/3 = 3x/3

329=x

329 miles

Answer:

Length of all 3 sides: 7, 7, and 9

Length of the two sides that have the same length: 7

Step-by-step explanation:

Let the two sides with equal lengths have a length of [tex]x[/tex]. We can write the third side as [tex]2x-5[/tex].

The perimeter of a polygon is equal to the sum of all its sides. Since the perimeter of the triangle is 23 meters, we have the following equation:

[tex]x+x+2x-5=23[/tex]

Combine like terms:

[tex]4x-5=23[/tex]

Add 5 to both sides:

[tex]4x=28[/tex]

Divide both sides by 4:

[tex]x=\frac{28}{4}=\boxed{7}[/tex]

Therefore, the three sides of the triangle are 7, 7, and 9 and the length of the two sides that have the same length is 7.

Answer:

x=12

Step-by-step explanation:

each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle

ex: 8*4=32 and 17*4=68

so we can assume that 15*4= 4x+12

60=4x+12

48=4x

x=12

Answer:

x = 12

Step-by-step explanation:

The triangles are similar so we can use ratios

4x+12      32

-------  = ------------

15             8

Using cross products

(4x+12) *8 = 15 * 32

(4x+12) *8 = 480

Divide each side by 8

(4x+12) *8/8 = 480/8

4x+12 = 60

Subtract 12 from each side

4x+12 -12 = 60-12

4x = 48

Divide by 4

4x/4 = 48/4

x = 12

Answer: 1865

Step-by-step explanation:

Given

Claimed strains of virus is 1700

If it is increased by 9.7%

Estimated value can be given by

[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]

Thus, the estimated number is [tex]1865[/tex]

Answer:

The answer is "Option C".

Step-by-step explanation:

This study looks after results including such illness growth during the trial time, and this includes additional elements such as suspected risk or source of protection (s). The study usually consists of taking and looking at such a cohort of subjects for a long time. The main advantage of these studies is knowledge accumulation and higher efficiency. Systematic reviews may suffer from choice distortion, in addition to the potential indication misinterpretation.

Answer:

401.92 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = (3.14) (4)^2 *8

V= 401.92

Answer:

They are equal

Step-by-step explanation:

4.5% is 0.045 in decimal form

Answer: They are equal

Step-by-step explanation:

I always remember by taking the two o's in percent and moving them two spots to the left and vise versa if you want to make a decimal into a percent  (move it two spots to the right).

Answer:

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.

The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.

The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).