A test is worth 80 points. multiple choice questions are worth2 points, and short- answer questions are worth 4 points. if the test has 25 questions, how many multiple- choice questions are there?a. the number of multiple choice questions times the number of short answer question is 25.b. the number of multiple choice questions plus the number of short answer question is 80.c. the number of multiple choice questions plus the number of short answer question is 25.d. the number of multiple choice questions minus the number of short answer question is 80.

Answer:

x = 135 degrees hopes this helps

Step-by-step explanation:

the whole triangle is equal to 180

180-41=139-94=45

so the missing angle in the triangle is 45

and that means the angle on the outside and the angle we just found 45 equals to 180

180-45=135

so 135 is the outside's missing angle

Answer: A

Step-by-step explanation:

\(\left(\frac{7}{8} \right)\left(-\frac{32}{49} \right)(14)(m^{2}n)(mn^{3})(mn^{2})=\boxed{8m^{4}n^{6}}\)

The 90% confidence interval is given by (3.9911; 7.9911)

It is 90% confident that the true average speed of a vehicle on a highway is between 3.9911 and 7.9911 miles per hour.

1) Former concept

A confidence interval is "a range of values ​​that is likely to encompass the values ​​of a population with some degree of confidence. Often expressed as a percentage.

The error bar is the range of values ​​above and below the sample statistic in the confidence interval.

A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean.

X = 2, represents the sample mean of the sample

μ = population mean (variable of interest)

s = 1 represents the standard deviation of the sample

n = 11 represents the sample size

2 ) Confidence Interval:

Confidence Interval for mean is given below:

                  X ± t (α/2) s/√n

To compute the critical value, we first need to find the degrees of freedom given by

df = n -1

   = 11 -1 = 10

Confidence is 0.90 or 90%, so the value of and is α = 0.1 , and α/2 = 0.05 you can use Excel, a calculator, or a spreadsheet to find the critical values. The Excel command would be "=-T.INV(0.05,10)".

2 - 1.81 (1/√11) = 3.9911

2 + 1.81 (1/√11) = 7.9911

So in this case the 90% confidence interval is (3.9911 , 7.9911)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 3.9911 and 7.9911 miles per hour.

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Answer:

AC line = DB line

Step-by-step explanation:

ac line is always larger that db line

Answer:

Step-by-step explanation:

(h)

\(KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}\)

(g)

\(s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v\)

(i)

\(s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t\)

(j)

\(\frac{pV}{T} =nR\\T=\frac{pV}{nR}\)

(k)

\(a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }\)

(i)sinθ\(=\frac{a}{b}\)

       θ=\(\frac{a}{sin(b)}\)

Answer:

x = 2 + √2

x = 2 - √2

Step-by-step explanation:

- x² + 2x + 1 = 0

x² - 2x - 1 = 0

Here,

a = 1

b = - 2

c = - 1

Now,

Discriminant

D = b² - 4ac

= (-2)² - 4(1)(-1)

= 4 + 4

= 8

=2√2 > 0

Real and Distinct roots

x = - b +- √b² - 4ac/2a

= - (-2) +- √ = (-2)² - 4(1)(-1)/2(1)

= 2 +- √4 + 4/2

= 2 +- √8/2

= 2 +- 2√2/2

= 2 +- √2

x = 2 + √2 or x = 2 - √2

Answer:

x = 2 + √2 or x = 2 - √2

Step-by-step explanation:

Edge 2021

The Taylor polynomials \(p_{4}\) and \(p_{5}\) centered at \(a = \frac{\pi}{6}\) for f(x) = 5cos(x) are:

\(p_{4}(x) = \frac{ 5\sqrt{3}}{2} - \frac{5}{2} (x - \frac{\pi }{6}) - \frac{ 5\sqrt{3}}{4} (x - \frac{\pi }{6})^2+ \frac{5}{8}(x - \frac{\pi }{6})^3+ \frac{ 5\sqrt{3}}{48}(x - \frac{\pi }{6})^4\)\(p5(x) = p_{4}(x) = \frac{ 5\sqrt{3}}{2} - \frac{5}{2} (x - \frac{\pi }{6}) - \frac{ 5\sqrt{3}}{4} (x - \frac{\pi }{6})^2+ \frac{5}{8}(x - \frac{\pi }{6})^3+ \frac{ 5\sqrt{3}}{48}(x - \frac{\pi }{6})^4 - \frac{5}{384}(x - \frac{\pi }{6} )^6\)

To find the Taylor polynomials centered at \(a = \frac{\pi}{6}\) for f(x) = 5cos(x), we need to find the derivative of the function at \(x = \frac{\pi}{6}\).  The first derivative of f(x) = 5cos(x) is -5sin(x), and the second derivative is -5cos(x).

Evaluating these derivatives at \(x = \frac{\pi}{6}\) gives us

\(-5sin(\frac{\pi }{6}) = -\frac{5}{2}\) and \(-5cos(\frac{\pi }{6}) = -\frac{5\sqrt{3} }{2}\).

The Taylor polynomial \(p_{4}(x)\) is then constructed using these derivatives and the powers of \(x - \frac{\pi}{6}\) up to the fourth power.

Similarly, for \(p_{5}(x)\), we add the fifth derivative term. Simplifying the expressions gives us the Taylor polynomials \(p_{5}(x)\) and \(p_{4}(x)\) center \(= \frac{\pi }{6}\) for f(x) = 5cos(x).

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Answer:

Its d

Step-by-step explanation:

because you square 10 and you get 100 and you have to multiply 6 with 100 which is 600 and then you multiply the 3.14 which gives you 1,884

PLEASE MARK AS BRAINLIEST

Answer:

x = 83°

Step-by-step explanation:

the 3 angles above the straight line sum to 180° , that is

41° + blank  + 56° = 180°

97° + blank = 180° ( subtract 97° from both sides )

blank = 83°

x and blank are vertically opposite angles and are congruent , then

x = 83°

Answer: 83 degrees

Step-by-step explanation:

Vertical angles have the same value and all of the angles add up to 360 degrees. Therefore we can create the equation:

2x+56+56+41+41 = 360

2x = 360-194

2x = 166

  x = 83

Angle x is 83 degrees

Note that Im just a student if I did this wrong pls correct me

Answer:

Step-by-step explanation:

The value of x and 2x must add to 180 to make the lines parallel

x + 2x = 180    Combine

3x  = 180         Divide by 3

3x/3 = 180/3

x = 60

Answer:

cant give you a answer but theres this app called gauth math try that its really helpful

Step-by-step explanation:

The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

the algebraic expression given in the question is a linear equation in three variables that are x , y and z and the simplification of this algebraic expression would also contain all the three variables

To solve this question we have to use the algebraic of  distributive property of addition over multiplication

so, using the above property and substituting the values given in the question we get

6x(3y +4z) = 6x(3y) + 6x(4z)

                  = 18 xy + 24 xz

Hence, The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

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Answer:

Approximately 494,314 people

This is an exponential growth question, specifically population growth. We will use the following equation to help us solve this situation:

P(t) = a(1+r)t

P(t) = total population (??)

a = initial population = 260,000

r = growth factor (the percent as a decimal) = 0.055

1 + r = 1 + 0.055 = 1.055

t = time in years = 12

So, we can substitute all our information and solve:

P(12) = 260,000(1.055)12 = 494,313.95

Rounding to the nearest whole person, 494,314 people in 12 years.

Answer:

X = -5

Step-by-step explanation:

See image for explanation

Answer:

A solution set is the set of values which satisfy a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality.

Answer: A. 397 miles

Step-by-step explanation:

Add the miles traveled on Saturday and Sunday to find out how many miles were traveled in total.

409 + 239 = 648

Now, subtract the total number of miles traveled from the original distance.

1,045 - 648 = 397

Answer:

397

Step-by-step explanation:

To figure this out, you just minus how much they have already traveled by the total distance they need to travel. To solve it, you can add together 409+239=648. Then, you take 648 and minus that from 1045. And so, 1045-648=397

The Wilcoxon signed-rank test is employed to see if there is a substantial difference between two related samples. Here the new cognitive therapy group and placebo group are related samples as they both belong to the same sample of cognitive therapy's study. The Wilcoxon signed-rank test is performed on the rank-based data as the data is not normally distributed. Following is the calculation for Wilcoxon’s signed rank test:The null hypothesis for the Wilcoxon signed-rank test is that there is no difference between the new cognitive therapy and placebo treatments. While the alternative hypothesis is that there is a difference between the two treatments.

The Wilcoxon signed-rank test is performed as follows:
Rank all the data, with the lowest value being ranked 1 and the highest value being ranked 12.
Calculate the difference between the new cognitive therapy and placebo group scores.
Take the absolute values of the differences.
Rank the differences in ascending order and ignore the signs.
Calculate the sum of the ranks of the new cognitive therapy group.
Calculate the test statistic T.
For this dataset, the calculations of the Wilcoxon signed-rank test are as follows:
Data Ranked (New therapy) Difference Absolute Difference Ranked Differences + Rank Therapy Differences - Rank Placebo 5 1 4 3 4 4 6 2 4 4 2 2 4 4 8 7 1 1 1 12 10 2 2 3 5 1 6 13 12 1 8 7 7 4 4 1 5 5 5 1 14 13 1 2 1 15 7 8 7 7 5 9 10 3 5 8 56 12 44 12 12 11 7 Total 49
Calculating T:

\($$T =\) \(\frac{Total\ of\ positive\ ranks - \frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$$\)

Here, n is the number of pairs, which is 12.
T = 3.52
Using the Wilcoxon signed-rank test table, the critical value at the 0.05 level for n = 12 is 18.
Since T (3.52) is less than the critical value (18), the null hypothesis cannot be rejected.
There is no evidence to suggest that there is a difference between the new cognitive therapy and placebo treatments.

Answer: 4x + 3 = 39

Step-by-step explanation:

Because you don't know how much each pizza costs, you can write it as x.

You multiply x by 4 to get 4x and add 3 because thats how much the chips cost.

That added up should equal 39 because thats how much he spent.

Answer: The answer is C ( 4x + 3 = 39 )

Step-by-step explanation:

4 = number of Pizzas. x = price of pizza. 3 = price of chips. 39 = total of 4 pizzas and chips together.

1) 4x + 3 = 39

2) 4x = 39 - 3

You will seperate the variable(4x) and the constants(3 and 9) So, you move (+3) to the other side making it negative. Then, you subtract (39-3) which will equal to (36)

4) 4x = 36

5) x = 36/4

You want to move the coefficient(4) to the other side. Thus, will make it a division becaue the oppisite of multiplication is division. So you cancel it out from x because 4/4 is 1.

6) x = 9

You divided 36/4 which will equal to 9

7) 4(9) + 3 = 39

Answer:

0

Step-by-step explanation:

Given

a + 7(a + b) - 8(a + b) + b ← distribute both parenthesis

= a + 7a + 7b - 8a - 8b + b ← collect like terms

= a + 7a - 8a + 7b - 8b + b

= 0

Answer:

0

Step-by-step explanation:

a+7a+7b-8a-8b+b

combining like terms

a+7a-8a+b+7b-8b

8a-8a+8b-8b

0

(a) The projectile reaches a height of 240 ft at t = 3 seconds and t = 5 seconds.  (b) The projectile returns to the ground at t = 0 seconds (initial launch) and t = 8 seconds.

(a)To find the time(s) when the projectile reaches a height of 240 feet and returns to the ground, we can set the height equation equal to the desired heights and solve for time.

Reach a height of 240ft:

Setting the equation s = -16t^2 + V0t equal to 240 and solving for t:

-16t^2 + V0t = 240

Since we know V0 = 128 ft/s, we substitute it into the equation:

-16t^2 + 128t = 240

Rearranging the equation:

16t^2 - 128t + 240 = 0

We can divide the equation by 8 to simplify it:

2t^2 - 16t + 30 = 0

Factoring the equation:

(2t - 6)(t - 5) = 0

Setting each factor equal to zero and solving for t:

2t - 6 = 0   -->   t = 3

t - 5 = 0   -->   t = 5

Therefore, the projectile will reach a height of 240 ft at two times: t = 3 seconds and t = 5 seconds.

(b) Return to the ground when V0 = 128 feet per second:

To find the time when the projectile returns to the ground, we set the height equation equal to zero:

-16t^2 + V0t = 0

Substituting V0 = 128 ft/s into the equation:

-16t^2 + 128t = 0

Factoring out a common term:

-16t(t - 8) = 0

Setting each factor equal to zero and solving for t:

-16t = 0   -->   t = 0 (initial time, launch)

t - 8 = 0   -->   t = 8

Therefore, the projectile returns to the ground at two times: t = 0 seconds (initial launch) and t = 8 seconds.

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Answer:

2

Step-by-step explanation:

Pick any point

You go up 2 and 1 over

2/1 is the same as 2 just simplified!

Answer:

around 81.2 degrees

Step-by-step explanation:

use inverse tangent

remeber tan = O/H

divide it first

84/13

6.461538461538462

then use invese tan(\(tanx^{-1}\))

81.20258929000894

or around 81.2 degrees

Answer:

d=20

Step-by-step explanation:

To find the distance between 2 points we use the distance formula

d = √(x2 - x1)²+(y2 - y1)²

The given points are (x1= -8, y1 = -6) and (x2 = 4, y2 = 10).

Substitute the given points into the distance formula.

d = √(4 + 8)²+(10 +6)²

d = √144+252

d= √400

d = 20

Answer: C

Explanation:

The range of a function is the set of all values of y that satisfy the function. On the graph, it is between the lowest value of y at the bottom and the highest value of y at the top. Looking at the graph, it extends to negative infinity at the bottom and the maximum value at the top y = 4

Thus, in interval notation,

Range = (- ∞, 4]

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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The area of the region bounded by

\[y=\frac{7}{(4+x)^2}+\frac{5}{7+x^2},\ y=0,\ x\ge5\]is 0.0188 (rounded to four decimal places).

Here's how to get the solution:

We are asked to find the area of the region bounded by the two curves.

The curves intersect at (5, 0) because x can not be less than 5.

They meet again at the point x ≈ 1.281.

Now, we must find the integrals for both functions in the given range.

We'll call the first function "f (x)" and the second "g (x)."

f(x) = 7 / (4 + x)² + 5 / (7 + x²)

g(x) = 0

The area between the two curves is obtained by finding the integral of the difference of the two functions.

The area is given by:

\[\int_{5}^{1.281} [f(x) - g(x)] dx\]

Since there is no point of intersection beyond x ≈ 1.281, we will use this value for the limit of integration.

Integrating:

\[\begin{aligned} &\int_{5}^{1.281} [f(x) - g(x)] dx \\ =& \int_{5}^{1.281} \left[\frac{7}{(x+4)^2}+\frac{5}{x^2+7}-0\right] dx \\ =& -\left[\frac{7}{4+x}+\sqrt{7}\tan^{-1}\left(\frac{x}{\sqrt{7}}\right)\right]_{5}^{1.281} \\ =& 0.0188. \end{aligned}\]

Thus, the area of the region is 0.0188.

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The location on the number line to plot the sum of the given number is shown in the image attached below.

In Mathematics, a number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Note: Each interval on this number line represents 1/10.

Next, we would add the given numbers together as follows:

Number = −1 3/10 + 2/5

Number = −13/10 + 2/5

Number = (-13 + 4)/10

Number = -9/10 or -0.9.

Therefore, the sum would be located between -4/5 and -1.

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Step-by-step explanation:

hope it is helpful to you

The true statement about the end behavior of f(x) is (b)

The equation of the function is given as;

f(x) = -4x^6 +6x^2-52

The leading coefficient of the above function is

Leading coefficient = -4

-4 is less than 0 i.e. negative

This means that options (a) and (c) are false

Also;

The ends of even functions face the same direction, and not opposite directions.

Hence, the true statement about the end behavior of f(x) is (b)

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