In the equation 2x + 7 = 21, what is the value of x?
A.7 B.9 C.11 D.14

The equation that shows the cost of x gallons of gas is given as y = 2x

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the cost of x gallons of gas. Gas costs $2 per gallon, hence:

y = 2x

The equation that shows the cost of x gallons of gas is given as y = 2x

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Answer:

a) [tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]

[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]

[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]

b) [tex]a=59 +1.96*3=64.88[/tex]

And for the other limit we have:

[tex]a=59 -1.96*3=53.12[/tex]

And we will have 95% of the values between (53.12, 64.88)

Step-by-step explanation:

Part a

Let X the random variable of interest of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(59,3)[/tex]  

Where [tex]\mu=59[/tex] and [tex]\sigma=3[/tex]

We are interested on this probability :

[tex]P(53<X<62)[/tex]

And we can solve this using the z score:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the last formula we got:

[tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]

And we can find this probability with this difference:

[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]

And uing the normal standard distribution or excel we got:

[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]

Part b

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.025[/tex]   (a)

[tex]P(X<a)=0.975[/tex]   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.96.

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.975[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.975[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=1.96<\frac{a-59}{3}[/tex]

And if we solve for a we got

[tex]a=59 +1.96*3=64.88[/tex]

And for the other limit we have:

[tex]a=59 -1.96*3=53.12[/tex]

And we will have 95% of the values between (53.12, 64.88)

In a normal distribution with mean 59 and standard deviation 3, approximately 81.85% of the data lie between 53 and 62. And about 95% of the data lie between 53 and 65, which is two standard deviations from the mean.

In a normal distribution, about 68% of the data lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% within three standard deviations.

Part A:

The range from 53 to 62 in this case is from -2 standard deviations from the mean (56) to +1 standard deviation (62). Looking at the empirical rule, we find that about 34.13% of data fall between the mean and -1 standard deviation, and 13.59% fall between -1 and -2 standard deviations. Similarly, about 34.13% of the data fall between the mean and +1 standard deviation. Therefore, the total percentage of data lying between 53 and 62 would be

34.13% + 13.59% + 34.13% = 81.85%, so option B is the closest.

Part B:

About 95% of the data lie between two standard deviations from the mean. Therefore, you would add and subtract two times the standard deviation from the mean, which would yield 59 - 2(3) = 53 and 59 + 2(3) = 65. Thus, about 95% of the data lie between 53 and 65.

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Answer:

24.5

Step-by-step explanation:

First, I subtracted 50 from 75.

75 - 50 = 25

Then, subtract 0.5 from 25.

25 - 0.5 = 24.5

I hope this helps!

Answer:

Only the x-value changes.

Step-by-step explanation:

When a point is reflected over the y-axis, it is the x-axis number that will flip it's sign.

When a point is reflected over the x-axis, it is the y-axis number that will flip it's sign.

~

Answer:

0.103 is the correct answer give me brainliest pls

Step-by-step explanation:

Final answer:

To find the critical value for a sample size of 3 and a 95% confidence level, you use a statistical table with an alpha value of 0.05, obtaining 5.991 as the critical value.

Explanation:

The critical value corresponding to a sample size of 3 and a confidence level of 95% is 5.991.

To find this critical value, we use a standard statistical table where for a 95% confidence level, the alpha value (a) is 0.05. Look up a table of critical values for a significance level of 0.05 and a sample size of 3 to obtain 5.991 as the critical value for a two-tailed test.

Answer:

Bar graph

Step-by-step explanation:

Step-by-step explanation:

The given equation is y = 23.67x + 13.12, where y is the value of the stock ABC and x is the number of days. The r-value of 0.9957 indicates a strong positive correlation between the two variables, which suggests that the equation is a good fit for predicting the value of the stock.

To find the value of the stock ABC at x = 28 days, we need to substitute x = 28 into the equation and solve for y:

y = 23.67(28) + 13.12

y = 663.76 + 13.12

y = 676.88

Therefore, the predicted value of the stock ABC at x = 28 days is $676.88.

The closest answer option is D. 675.88, but the correct answer is actually slightly higher at $676.88.

We are given a linear equation y = 23.67x + 13.12, where 'x' is the number of days and 'y' is the stock value.

Now, we need to predict the stock value for 'x' equals to 28 days. To do so, we substitute x = 28 into the equation.

Start by multiplying the given value of x with the slope:
23.67 times 28 equals 662.76.

Next, add the y-intercept to the result from the first step. So you take 662.76 and you add 13.12.
The sum is 675.88.

So, according to our calculation, the ABC stock would be worth 675.88 on the 28th day.

So, the answer is

Answer: D. 675.88.

Answer:

They both equal 30, so if the question is are both equal the statement is true!

Note: I would appreciate if you give me 5 stars, a thanks, and brainiest :)

Answer:

16 cups

Step-by-step explanation:

If Joanna bought a gallon container of milk at the store then  volume of the container in cups is 16.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Joanna bought a gallon container of milk at the store.

We need to find the  volume of the container in cups

1 cup= 8 ounces

1 gallon =128 ounces

So divide 128 by 8

128/8

8 is the common divisor  for 128 and 8

So divide both numerator and denominator by 8

We get 16 cups

Hence, the volume of the container in cups is 16.

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Answer:

(a) (x + 3)(2x + 7) = 0

(b) These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.

Step-by-step explanation:

(a) We set 4x² -26x + 42 equal to 0:

4x² -26x + 42 = 0

Let's divide both sides by 2 to simplify this a bit:

2x² - 13x + 21 = 0

Now, we need factors a and b of 2 and c and d of 21 such that ac + bd = -13. The factors of 2 are: 1 and 2, so let's say a = 1 and b = 2. The factors of 21 are: (1, 21), (3, 7), (-1, -21), and (-3, -7). We see that if c = -7 and d = -3, this works:

ac + bd = 1 * (-7) + 2 * (-3) = -7 - 6 = -13

So, the factored form is:

(x - (-3))(2x - (-7)) = 0

(x + 3)(2x + 7) = 0

(b) So now we need to solve this. Set each of the two parenthetical expressions equal to 0:

x + 3 = 0

x = -3

AND

2x + 7 = 0

x = -7/2

These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.

Answer:

a) 2(x - 3)(2x - 7) = 0

b) function is 0 when x = 3 or 7/2

Step-by-step explanation:

4x² - 26x + 42 = 0

2(2x² - 13x + 21) = 0

2[2x² - 6x - 7x + 21] = 0

2[2x(x - 3) - 7(x - 3)] = 0

2(x - 3)(2x - 7) = 0

Solutions:.

x = 3, 7/2

Answer: 21.67 and full Answer is 21.6732

Step-by-step explanation: $108.36 divide by 5!

Answer:

A

Step-by-step explanation:

a. type in 2⁻³ in the calculator and you get 0.125, which is 1/8.

b. Anything to the power of 0 will equal 1. :)

Answer:

A.

Step-by-step explanation:

a.

when you have a negative exponent, the simplified value becomes a fraction:

2^-3

1/2^3

1/8

b.

any number to the power of 0 is equal to one:

(5.5)^0

1

Hope this helps :)

Answer:

Its easy

Step-by-step explanation:

Just think and ask teachers for help math is easy if your good at anything else in school , then math should be easy it have to do with all that.

Volume of a Rectangular Prism:

V = lwh

Length: 12 centimeters

Height: 9 centimeters

Width: 2 centimeters

V = 12(9)2

V = 108 x 2

V = 216

V = 216cm^2

The volume of the prism is 216 cm³ with a length of 12 cm, a height of 9 cm, and a width of 2 cm. This is obtained by using the formula for the volume of a prism.

The volume of a prism is

V=B × h cm³

Where B is the base area of the prism and h is the height of the prism.

For the given prism,

length l=12cm

width w=2cm and

height h=9cm

Calculating the base area:

Since the prism has length and width, it is a rectangular prism

Thus,

B = l × w sq.cm

Then, the volume of the prism becomes

V= l × w × h cm³

On substituting the values

V= 12 × 2 × 9

  = 216 cm³  

Therefore, the volume of the given prism is 216 cm³.

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Answer:

The circumference of the green circle is about 138.23 meters.  

The circumference of the blue circle is about 69.115 meters.    

Step-by-step explanation:

Considering 22 m as the green circle radius and 11 m as the blue circle radius:

The circumference of the green circle is about:  

[tex]C=2\pi r[/tex]

[tex]C=2\pi 22\\C=44\pi \\C=138.23 m[/tex]

The circumference of the blue circle is about:  

[tex]C=2\pi r[/tex]

[tex]C=2\pi 11\\C=22\pi \\C=69.115 m[/tex]

Answer:

The volume of the cylinder is 432π

Step-by-step explanation:

Volume of a Cylinder is, πr²h where r = radius and h = height of the cylinder.

so, πr²h = π×6²×12 = 432π

Answered by GAUTHMATH

Answer:

A) 432

Step-by-step explanation:

Answer:

To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex. I had this question and got it right. Have a great day

Step-by-step explanation:

Answer:

The answer would be -17

Step-by-step explanation:

On evaluation of  19 - 11 + (-17) + (-19) + 11 will result in -17

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Using the concept that

+ - = -

On opening the brackets,

19 -11 + -17 + - 19 + 11=19-11-17-19+11

=19-19-17-11+11

=-17

Thus, 19 - 11 + (-17) + (-19) + 11 can be evaluated as -17

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Answer:

37

Step-by-step explanation:

This is a right triangle so we can find the lengths by using the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

12^2 + 35^2 = c^2

144 +1225 = c^2

1369 = c^2

Take the square root of each side

sqrt(1369) = sqrt(c^2)

37 =c

Answer:

95/3 = 31

31 ratio for 2 and 1 then make up the difference

there were 25 point and 45 ...1 point shots

but 32 x 3 makes 96 you will see the top answer is correct 25 2 points and 45 one points as we can distribute 50 and 45 easily as a fair 6/10 and 4/10 balance of 95 just like we do to find 60% of 95 or 40% of 95.

Hi Samantha heres an example for both questions see if you can try add the items and find a multiple to 95 for this question then divide by 3 and distribute like this example below which answers your other question about popcorn.

Step-by-step explanation:

462 = revenue

282 = amount sold

$1 = small

$3 = large

1. we add the amounts together = $4

2. We divide 462/4 =    460/4 = 115 so we are 2 out

3. In our workings we show 4 less +2 less = 4 x 115 = 460 +2 =462-6

456

111 = small $1

456-111 = 345 + 6 = 351 ( large $3 as we were 4+2 less we add 6 = 351

351/3 = 119 large. (we divide by price $3)

111 = small.(we keep)

To find equations

we know know on our workings we have 111 +351 we can call these s and l

s111 + l351 = s111 + l119

462 = 230

462/230 = 2sl mean price.

=====

We plug in again to find 1

462/230 + 1 = 2sl(+l)+x

1s x 1^2  x  1l^2 x x = 1     we rearrange the 1

1s x 1^2  x  3l   we replace ^2 with 1

1s  x 1 x 3l = 1

1 x 3l = 1/1s

3l = 1s

====

Now we can match s and l

3 / 1 + 4 = 460l

3 / 1 = 460/4l

3 / 1 = 120l  

1 x 120-3l

1  x 117l

117 ( 351/3) = L   you cna try rewriting this ( ) plug in in a new equation just added to show you how it works.

l = 357 = L  I wrote capitals as the l looked like a number.

When we subtract total  462- 351 = s then  s = 111

When you understand minus 6 may have made things more tricky try another number where the total 462 is rounded up by 3 to 465 or 470 an work in 30's and 10's then divide by 10 may be of some help/reflection to designing equations it helps you remember alternatives to find out distribution.

Answer: Jordana will need 92 feet of fencing

Step-by-step explanation:

Given: Length of rectangle = 28 feet

Width of rectangle = 14 feet

Diameter of semicircle = 14 feet

Therefore radius of semicircle : r = [tex]\dfrac{Diamater}{2} =\dfrac{AB}{2} =\dfrac{14}{2} =7 \text { feet }[/tex]

Now we have to find the perimeter of attached figure for putting fence around a garden

[tex]Perimeter = 2 Length +Width + \text {Circumference of semicircle }\\\\\Rightarrow Perimeter = 2\times AD+DC + \pi r\\\\\Rightarrow Perimeter = 2\times 28+14 +\dfrac{22}{7} \times 7 \\\\\Rightarrow Perimeter = 56+14+22 = 92 \text {feet}[/tex]

Hence, jordana will need 92 feet of fencing

Answer:

the answer is 92 (or C)

Step-by-step explanation:

I did the review

Answer:

  C.  A and E

Step-by-step explanation:

A function is increasing when any increase in x results in an increase in y. That is, the general direction is up to the right (/).

A function is decreasing when any increase in x results in a decrease in y. That is, the general direction is down to the right (\).

__

The given graph is increasing for the sections marked A and E. It is decreasing for the section marked C. It is neither increasing nor decreasing at the points B and D.

The appropriate choice for where the function is increasing is A and E.

Answer:

this hard

Step-by-step explanation:

Answer:

Can you provide a screenshot? I could help you better with a visual.

Answer: i believe it is 15n

Step-by-step explanation

Answer:

37.68 ft.

Step-by-step explanation:

Answer: [tex]37.68ft[/tex]

Step-by-step explanation:

[tex]Formula: C=\pi d[/tex]

Replace

[tex]C=(3.14)(12ft)\\C=37.68ft[/tex]

Answer:

[tex](5, \: - 2)[/tex]

Step-by-step explanation:

[tex]x + 3y = - 1 \\ 2x + 2y = 6 \\ solve \: the \: equation \\ \\ x = - 1 - 3y \\ 2x + 2y = 6 \\ substitute \: the \: value \: of \: x \: into \: an \\ equation. \\ \\ 2( - 1 - 3y) + 2y = 6 \\ distribute \\ \\ - 2 - 6y + 2y = 6 \\ add \: - 6y \: to \: 2y \\ \\ - 2 - 4y = 6 \\ add \: 2 \: from \: both \: sides \\ \\ - 2y = 8 \\ divide \: both \: sides \: by \: 2 \\ \\ y = - 2 \\ substitute \: the \: value \: of \: y \: into \: an \\ equation. \\ \\ x = - 1 - 3( - 2) \\ distribute \\ \\ - 1 + 6 \\ add \: - 1 \: to \: 6 \\ \\ x = 5 \\ \\ (5, - 2)[/tex]

Answer:

x2

1 x (N x 2)

2 x (1 x 2) = 4

2 x (4 x 2) = 16

Step-by-step explanation: