The circumference of a circular field is 163.28 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.

Answer:

18n+p-6

Step-by-step explanation:

you combine 12 and  6, then put the exponents in order

Hey there!

Like terms are "from the same family"

Let me clarify.

For example. we have an expression "2t+12h-6h"

In this case, 12h and -6h are like terms and 2t and 12h are not like terms.

Here's another example:

r+a-y+4+9-1

The like terms are:

4, 9, and -1

Now that we know what like terms are, let's identify the like terms in the given expression.

The expression is:

\(\bold{12n-6+p+6n}\)

What are the like terms?

That's right, 12n and 6n:

\(\bold{12n+6n-6+p}\)

\(\bold{18n-6+p}\)

Hence, the answer is

\(\boxed{\boxed{\bold{18n-6+p}}}\)

Hope everything is clear.

Let me know if you have any other questions; if so, please comment.

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\(\rule{250}{2}\)

Answer:

False,

Step-by-step explanation:

There is not enough information given.

The given statement - "All the races are 175 miles long" is true.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is to find whether all races are more than 175 miles or not.

All the races are 175 miles long. The given statement is true.

Therefore, the given statement - "All the races are 175 miles long" is true.

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Rewrite the limit as

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5\)

Then using the known limit,

\(\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1\)

it follows that

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}\)

Answer:

\(BC=5.1\)

\(B=23^{\circ}\)

\(C=116^{\circ}\)

Step-by-step explanation:

The diagram shows triangle ABC, with two side measures and the included angle.

To find the measure of the third side, we can use the Law of Cosines.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

In this case, A is the angle, and BC is the side opposite angle A, so:

\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)

Substitute the given side lengths and angle in the formula, and solve for BC:

\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)

\(BC^2=49+9-42\cos 41^{\circ}\)

\(BC^2=58-42\cos 41^{\circ}\)

\(BC=\sqrt{58-42\cos 41^{\circ}}\)

\(BC=5.12856682...\)

\(BC=5.1\; \sf (nearest\;tenth)\)

Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:

\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)

Substitute the values of the sides and angle A into the formula and solve for the remaining angles.

\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)

Therefore:

\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)

\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)

\(B=22.5672442...^{\circ}\)

\(B=23^{\circ}\)

From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):

\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)

\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)

\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)

\(180^{\circ}-C=63.5672442...^{\circ}\)

\(C=180^{\circ}-63.5672442...^{\circ}\)

\(C=116.432755...^{\circ}\)

\(C=116^{\circ}\)

\(\hrulefill\)

Additional notes:

I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

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

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Answer:

  -0.93

Step-by-step explanation:

You want to know a good estimate of the correlation coefficient for the data in the scatterplot shown.

The sign of the correlation coefficient will be the sign of the slope of the best-fit (trend) line. Here, the data generally trends downward, so the sign of the correlation coefficient is negative.

The magnitude of the correlation coefficient will be 1 if the data lies on a straight line. Here, the data does not lie on a line, so the correlation coefficient is not 1. The value -0.93 is a better guess.

__

Additional comment

We don't have enough experience with scatter plots to have an intuition about the magnitude of the correlation coefficient. The attached calculator output tells us this data has a correlation coefficient of about -0.93, which is the "not 1" answer choice.

#95141404393

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer: 17%

Step-by-step explanation: 83+17 = 100, 17/100 = 0.17 = 17%

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

t = 7.46, 0.42

Explanation:

h = 126t - 16t²    [ "h" is height, "t" is time ]

when height is 50 feet

==================

\(\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0\)

==================

\(\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}\)

\(\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}\)

\(\Longrightarrow \sf t = 7.46, \ 0.42\)

Let's find

Put h=50

Use quadratic formula

\(\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}\)

\(\\ \rm\Rrightarrow t=7.5s,0.4s\)

Answer: A

Step-by-step explanation:

The answer is choice A since it has the rise and run of 2/3.

Iris should use an income value of approximately $3,137.50 when making her budget.

When making her budget as a freelancer, Iris should use an income value that reflects her average earnings over the past four months. By calculating the average income, Iris can have a more stable and reliable estimate for her budget planning.

To determine the average income, Iris needs to add up the total income earned over the four months and divide it by the number of months. Summing up the income values, we get:

$2700 + $4600 + $3550 + $1700 = $12,550

Next, dividing the total income by four (the number of months), we find:

$12,550 / 4 = $3,137.50

Therefore, Iris should use an income value of approximately $3,137.50 when making her budget. This average value allows her to account for fluctuations in her monthly income and provides a more accurate representation of her earning potential.

It is important for Iris to consider her expenses and financial goals when budgeting. By using the average income, she can create a budget that balances her income and expenses, allowing her to allocate funds appropriately for various needs such as bills, savings, investments, and personal expenses.

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The probable question may be:

Iris is a working freelancer and has been tracking her monthly income for the last four months, which are $2700, $4600, $3550, and $1700. What income value should she use when making her budget?

Answer:

Explained below.

Step-by-step explanation:

The information provided is:

n = 200

X = 106

α = 0.05

The sample proportion is:

\(\hat p=\frac{X}{n}=\frac{106}{200}=0.53\)

(a)

A hypothesis test is to performed to determine whether more than half of all drivers drive a car made in this country.

The hypothesis is:

H₀: The proportion of drivers driving a car made in this country is less than or equal to 50%, i.e. \(\mu_{p}\leq 0.50\)

Hₐ: The proportion of drivers driving a car made in this country is more than 50%, i.e. \(\mu_{p}> 0.50\)

(b)

Compute the value of the test statistic:

\(Z=\frac{\hat p-\mu_{p}}{\sqrt{\frac{\mu_{p}(1-\mu_{p})}{n}}}\)

   \(=\frac{0.53-050}{\sqrt{\frac{0.50(1-0.50)}{200}}}\\\\=0.8485\\\\\approx 0.85\)

Compute the p-value as follows:

\(p-value=P(Z_{0.05}>0.85)\\=1-P(Z_{0.05}<0.85)\\=1-0.80234\\=0.19766\\\approx 0.198\)

*Use a z-table.

Thus, the p-value of the test is 0.198.

(c)

Decision rule:

Reject the null hypothesis if the p-value is less than the significance level.

p-value = 0.198 > α = 0.05

The null hypothesis will not be rejected.

The correct option is (A).

(d)

Conclusion:

There is not enough evidence at 0.05 level of significance to support the claim that the proportion of drivers driving a car made in this country is more than 50%.

for the first question, you get 576

for the second one you get 0.1875

If the Interest rates fluctuate with the economy. In the 1980s, the highest CD interest.

a. The ending balance is $2,225.54.

b. The ending balance is $1,105.17.

c. The difference is  $1,120.37.

a. Ending balance

Ending balance =pe^r×t

Where:

P= Principal = $1,000

R= Interest rate = 16%

T= Time = 5

Ending balance=?

Ending balance =1000e^0.16×5

Ending balance =1000e^0.8

Ending balance =$2,225.54

b. Ending balance:

Ending balance =pe^r×t

Where:

P= Principal = $1,000

R= Interest rate = 2%

T= Time = 5

Ending balance=?

Ending balance =1000e^0.02×5

Ending balance =1000e^0.1

Ending balance =$1,105.17

c. Difference :

Difference = $2,225.54 - $1,105.17

Difference = $1,120.37

Therefore the ending balance is $2,225.54, the ending balance is $1,105.17 and the difference is  $1,120.37.

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Answer: 0.5

Step-by-step explanation:

17 is half of 34 and 1/2 = 0.5

Answer: 0.5  is this second grade

Answer:

x=16, have a great day

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

13x + 7 = 215

13x = 208 (Subtract 7 from both sides.)

x = 16 (Divide both sides by 13)

Answer:

500 students

Step-by-step explanation:

40% = 200 students

divide both by 4 to 10%

10% = 50

multiply both by 10 to get 100%

100% = 500

or the quicker way,

200 x 2 = 400 (80%) + 100 (20%) = 500 (100%)

Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

Answer:

\(\frac{8342}{10000} \\ \)

Answer C is correct

Step-by-step explanation:

\(0.8342 = \frac{8342}{10000} \)

To check whether this correct or wrong.

\(0.8342 \times 10000 = 8342\)

hope this helps

brainliest appreciated

good luck! have a nice day!

The decimal 0.8342 expressed as a fraction is (c) 8342/10000

From the question, we have the following parameters that can be used in our computation

The decimal 0.8342

Express the decimal 0.8342 as a fraction

So, we have the following representation

Fraction = 8342/10000

When the fraction is simplified, we have

Fraction = 8342/10000

Hence, the decimal 0.8342 as a fraction is (c) 8342/10000

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Answer:

R = 3.813% per year.

Step-by-step explanation:

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

The following goodness-of-fit metrics were looked at in order to choose the top model: (a)the standard error of the estimate, (b)the coefficient of determination, and (c)the adjusted coefficient of determination.

The degree to which the model fits the data points is indicated by the standard error of the estimate. It is the typical discrepancy between the values that were observed and those that were projected. The model fits the data more accurately the lower the estimate's standard error.

R-squared, also referred to as the coefficient of determination, is another metric for goodness-of-fit.

The number of independent variables in the model is taken into consideration in a modified version of the coefficient of determination known as the adjusted coefficient of determination. Models with a lot of variables that don't significantly enhance fit are penalised.

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The complete question is :

In order to select the preferred model, we examine several goodness-of-fit measures: Select all goodness-of-fit measures examined!

Multiple select question.

(a)The standard error of the estimate

(b)The coefficient of determination

(c)The adjusted coefficient of determination

(d)The standard coefficient

Answer:

90

Step-by-step explanation:

the angle of a straight line is 180. So, take 65 and 25 away from 180:

180-65-25=90

C=90

Hope this helps

By the SSS Congruence Theorem, △ABC ≅ △DEF.

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

What is the SSS rule?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

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Answer:

7, 23, and 20

Step-by-step explanation:

Okay, let's go through this. We know that the perimeter is 50 and the perimeter must be all the sides added together. let's write that down

n + 4n - 5 + 2n +6 = 50

Let's combine like terms

7n + 1 = 50

subtract 1 from each side

7n = 49

Divide both sides by 7

n = 7

We know that one of the sides is n, so part of our answer is 7. Now let's plug in n for the other values

4(7) - 5 = 23

2(7) +6 = 20

The answer is 7, 23, and 20

Answer:

Therefore, in a scenario where mass is decreased, an increase in kinetic energy is possible if velocity increases. In the case of a decrease in mass and velocity, kinetic energy must decrease because both of the determining factors decreased.

Step-by-step explanation:

Step-by-step explanation:

Decreases in mass cause decreases in kinetic energy due to the aforementioned positive relationship between the two. ... In the case of a decrease in mass and velocity, kinetic energy must decrease because both of the determining factors decreased.