MP and MN are tangents to the circle.What is the value of x?133M94°90Nxo17286

answers 800 cm k=240 ZI=173°

Answer:

a

  \(z_t = -1.645\)

b

 We should reject the Upper  \(H_o\)

Step-by-step explanation:

From the question we are told that

   The test statistics is     \(t_s = -3.43\)

     The probability is   \(p < 0.39\)

      The level of significance is \(\alpha = 0.05\)

Now looking at the probability we can deduce that this is a left tailed test

The  second step to take is to obtain the critical value of \(\alpha\) from the critical value table  

    The value  is  

               \(t_ {\alpha } = 1.645\)

Now  since this  test is  a  left tailed test  the critical value will be

               \(z_t = -1.645\)

This because we are considering the left tail of the normal distribution curve

 Now  since the test statistics falls within the  critical values the Null hypothesis is been rejected

Answer:

multiply numbers ADD exponents

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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The value of \(Cos(A - B)\) will be \((\frac{-\sqrt{5} }{5} )\).

Trigonometric functions are  the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

We have,

\(Sin(A) = \frac{4}{5}\) ,    \(\frac{\pi }{2} < A < \pi\)

\(Sin(B) = \frac{-2\sqrt{5} }{5}\) ,   \(\pi < B < \frac{3\pi }{2}\)

So,

Using identity ;

\(Cos(A - B)= CosA\ *\ Cos B + Sin A\ *\ Sin B\)

So,

First find \(SinB\) and \(CosA\);

i.e.

\(CosB=\frac{-\sqrt{5} }{5}=\frac{-1}{\sqrt{5} }\),   \(\pi < B > \frac{3\pi }{2}\)

\(CosA=\frac{-3}{5}\),    \(\frac{\pi }{2} < A > \pi\)

Now,

Substituting values,

\(Cos(A - B)= CosA\ *\ Cos B + Sin A\ *\ Sin B\)

\(Cos(A - B)= ((\frac{-3}{5})\ *\ \frac{-1}{\sqrt{5}} ) +((\frac{4}{5})\ *\ \frac{-2\sqrt{5} }{5} )\)

Simplify,

\(Cos(A - B)= (\frac{3 }{5\sqrt{5}} ) -(\frac{8 }{5\sqrt{5}})\)

\(Cos(A - B)= (\frac{-5 }{5\sqrt{5}} )\)

\(Cos(A - B)= (\frac{-1 }{\sqrt{5}} )\)

Or we can write

\(Cos(A - B)= (\frac{-\sqrt{5} }{5} )\)

Hence, we can say that the value of \(Cos(A - B)\) will be \((\frac{-\sqrt{5} }{5} )\) which is given in option (b).

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Answer: x = 52, y = 128, z = 52

Step-by-step explanation:

The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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Total number of people surveyed = 118

Number of people who own dogs = 78

Number of people who own cat = 44

Number of people who own both cats and dogs = 26

Number of people who only own dogs = 78 - 26 = 52

Number of people who own only cats = 44 - 26 = 18

Only dog owners + Only cat owners + Both + Neither = Total people surveyed

52 + 18 + 26 + Neither = 118

Neither = 22(answer)

Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Answer:

288

Step-by-step explanation:

Hope it helps :>

Answer:

288

Step-by-step explanation:

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Answer:

I'm not exactly sure what this is asking, so i'm going to answer each part

A. 44%
B. 27%
C. 11.88% (assuming independence)

D. 61.36%

Step-by-step explanation:

Honestly I'm not really sure what he's asking but for A and B the answer is in the question. For C i assumed independence and multiplied the respective probabilities. For D I divided .27/.66 since it is a dependency probability

The probabilities of the events are

a. 0.44

b. 0.27

c. 0.1188

d. 0.2444.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Statistics classes require a statistical calculator = 44% = 0.44

Statistics classes require a computer that has statistical software = 27% = 0.27

Of the classes that require a statistical calculator, classes also require the use of a computer = 15% = 0.15

a. P(Statistical Calculator) = 0.44

b. P(Statistical Software) = 0.27

c. P(Require a Statistical Calculator and Statistical Software) = \((0.44)(0.27)\)

⇒ \(0.1188\)

d. P(Require a Statistical Calculator GIVEN Require Statistical Software)

⇒ \(\frac{0.066}{0.27}\)

⇒ \(0.244\)

Hence we can conclude that the probabilities of the events are

a. 0.44

b. 0.27

c. 0.1188

d. 0.2444.

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Answer:

m=2

Step-by-step explanation:

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Subtract 4x  from both sides of the equation.

−2y=5−4x

Divide each term by −2 and simplify.

y=2x−5/2

Answer:

$2.79

Step-by-step explanation:

We know

Peter bought a sandwich for $4.25, a drink for $2.17, and a cookie for $0.79.

4.25 + 2.17 + 0.79 = $7.21

If he paid with a $10 bill, how much change did Peter get?

10 - 7.21 = $2.79

So, Peter get $2.79 in change.

Step-by-step explanation:

first

(0.8a+0.4b)^2= (0.8a+0.4b) *(0.8a+0.4b)

=

0.64 a^2 + 0.32 ab +0.32ab + 0.16 b^2=

0.64 a^2 + 0.64ab + 0.16 b^2

second

(0.8a-0.4b)^2+1.28ab

= 0.64 a^2 - 0.64ab +0.16 b^2 + 1.28ab

= 0.64 a^2 + 0.64ab + 0.16 b^2

since the first (left parameters ) equals the second(right side parameters)

approved✓✓

Step-by-step explanation:

The interquartile range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. It is a measure of the spread or variability of the middle 50% of the data.

To calculate the interquartile range, you need to first arrange the dataset in ascending order. Then, find the median (Q2) of the entire dataset. Next, find the median of the lower half of the dataset, which is called the first quartile (Q1). Finally, find the median of the upper half of the dataset, which is called the third quartile (Q3).

The interquartile range is then calculated by subtracting Q1 from Q3: IQR = Q3 - Q1.

The IQR is useful because it provides a measure of the spread of the middle 50% of the data, which can help identify outliers or extreme values. It is less affected by extreme values compared to the range, making it a robust measure of dispersion.

if you have data :

1 2 3 4 5 6 7 8 9 10 11

lower quartile is 3

upper quartile is 9

Interquartile Range = 9 − 3 = 6

Interquartile Range is what you get when you

subtract the middle numbers

quartile has the word quart like quarter or 1/4

quartiles divide a list of numbers into three quarters

if you have

1 2 3 4 5 6 7 8 9 10 11

The middle quartile (or median), Q2, is the middle number in the set. It divides the set in two halves.

The lower quartile, Q1, is the middle number of the bottom half. It divides the bottom half in two.

The upper quartile, Q3, is the middle number of the top half. It divides the top half in two.

Subtract the lower quartile from the upper quartile  = Interquartile Range

Interquartile Range = 9 − 3 = 6

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Answer:

\((a)\ \bar x_1 - \bar x_2 = 2.0\)

\((b)\ CI =(1.0542,2.9458)\)

\((c)\ CI = (0.8730,2.1270)\)

Step-by-step explanation:

Given

\(n_1 = 60\)     \(n_2 = 35\)      

\(\bar x_1 = 13.6\)    \(\bar x_2 = 11.6\)    

\(\sigma_1 = 2.1\)     \(\sigma_2 = 3\)

Solving (a): Point estimate of difference of mean

This is calculated as: \(\bar x_1 - \bar x_2\)

\(\bar x_1 - \bar x_2 = 13.6 - 11.6\)

\(\bar x_1 - \bar x_2 = 2.0\)

Solving (b): 90% confidence interval

We have:

\(c = 90\%\)

\(c = 0.90\)

Confidence level is: \(1 - \alpha\)

\(1 - \alpha = c\)

\(1 - \alpha = 0.90\)

\(\alpha = 0.10\)

Calculate \(z_{\alpha/2}\)

\(z_{\alpha/2} = z_{0.10/2}\)

\(z_{\alpha/2} = z_{0.05}\)

The z score is:

\(z_{\alpha/2} = z_{0.05} =1.645\)

The endpoints of the confidence level is:

\((\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\)

\(2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}\)

\(2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}\)

\(2.0 \± 1.645 * \sqrt{0.0735+0.2571}\)

\(2.0 \± 1.645 * \sqrt{0.3306}\)

\(2.0 \± 0.9458\)

Split

\((2.0 - 0.9458) \to (2.0 + 0.9458)\)

\((1.0542) \to (2.9458)\)

Hence, the 90% confidence interval is:

\(CI =(1.0542,2.9458)\)

Solving (c): 95% confidence interval

We have:

\(c = 95\%\)

\(c = 0.95\)

Confidence level is: \(1 - \alpha\)

\(1 - \alpha = c\)

\(1 - \alpha = 0.95\)

\(\alpha = 0.05\)

Calculate \(z_{\alpha/2}\)

\(z_{\alpha/2} = z_{0.05/2}\)

\(z_{\alpha/2} = z_{0.025}\)

The z score is:

\(z_{\alpha/2} = z_{0.025} =1.96\)

The endpoints of the confidence level is:

\((\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\)

\(2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}\)

\(2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}\)

\(2.0 \± 1.96 * \sqrt{0.0735+0.2571}\)

\(2.0 \± 1.96* \sqrt{0.3306}\)

\(2.0 \± 1.1270\)

Split

\((2.0 - 1.1270) \to (2.0 + 1.1270)\)

\((0.8730) \to (2.1270)\)

Hence, the 95% confidence interval is:

\(CI = (0.8730,2.1270)\)

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

Answer:

39  shelves needed to build

Step-by-step explanation:

To find the number of shelves needed we need to divide the number of mystery books by 34

We know that. Each shelf can hold 34.

It is given that, There are 1,326 mystery books

So, 1,326/34

39  shelves needed to build

Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Answer:

00h08

Step-by-step explanation:

eight minutes passed twelve

Complete Question

A batter hits a baseball 3 ft above the ground toward the center field fence, which is 10 ft high and 400 ft from home plate. The ball leaves the bat with speed at 115 an angle 50 above the horizontal. Is it a home run?

Answer:

\(t=5.40sec\)

Step-by-step explanation:

From the question we are told that

Height on hit \(H_h=3ft\)

Height of center field fence \(H_f=10ft\)

Distance from home plate \(D=400ft\)

Initial speed \(v_0=115\)

Angle  \(\theta=50\)

Generally the Parametric equation of the trajectory of a projectile are mathematically represented as

\(x=(v_0cos\theta )t\)

\(y=(v_0sin\theta )t-\frac{1}{2} gt^2\)

Therefore

\(x=(v_0cos\theta )t\)

\(x=(115cos50\textdegree )t\)

\(x=74t\)

\(y=(v_0sin\theta )t-\frac{1}{2} gt^2\)

Initial co_ordinates (0,3)

\(y=3+(115sin50\textdegree )t-\frac{1}{2} 32t^2\)

\(y=3+88t-16t^2\)

Generally its a home run when Y>10 and x=400

Time when x=400 is

\(t=\frac{400}{74}\)

\(t=5.40sec\)

The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

Option B is the correct answer.

We have,

From the graph plot,

We see that,

The y-intercept is when x = 0.

This means,

At 0 hours, the amount of diet soda is 40.5.

Now,

y = 40.5 means the machine starts with 40.5 ounces of diet soda.

Thus,

The y-intercept is 40.5 the machine starts with 40.5 ounces of diet soda.

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The red dot on the graph is (2, -8)

The domain of the function consists of all real numbers greater than 0.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

Next, we would determine the function which models the amount of gas as follows:

Function, f(x) = rate × x

Function, f(x) = 2.25 × x

Function, f(x) = 2.25x

Based on the function above, we can reasonably and logically deduce that the amount of gas cannot be negative. Therefore, the domain of this function is given by:

Domain = [0, ∞]

In conclusion, the domain is equal to all real numbers that are greater than zero (0).

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The requried fraction of the registered voters who didn't vote is given as 2/5.

Fraction is defined as the number of compositions that constitutes the Whole. Fraction is generally denoted as a / b, where a = numerator and b = denominator.

In a certain state about 3/5 of registered voters participated in the 2016 election.
Let the fraction of registered voters to did not vote to be x,
So,
According to the question,
1 = 3/5 + x
x = 1 - 3/5
x = 2 / 5

Thus, the requried fraction of the registered voters who didn't vote is given as 2/5.

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Answer:

n = 18

Step-by-step explanation:

n/2 + 15 = 24

n/2 = 9

n = 18

The kite is approximately 345 feet above the ground.

The height of the kite above the ground is 287 ft

The length of the string, the height of the kite (h) above ground and the perpendicular distance from the end of the kite string to the man forms a right angled triangle.

Trigonometric shows the relationship between the lengths and angles of a right angled triangle.

Therefore using trigonometric ratios:

sin(55) = h / 350

h = 287 ft

Therefore the height of the kite above the ground is 287 ft.

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Answer:

4.647 to the nearest thousandth.

Step-by-step explanation:

The formula for the length of an arc between  x = a and x = b is

  a

    ∫  √( 1 + (f'(x))^2) dx

  b

Here f(x) = √x so

we have  ∫  (√( 1 + (1/2 x^-1/2))^2 )   between x = 0 and x = 4.

=   ∫ ( √( 1 + 1/(4x)) dx   between  x = 0 and x = 4.

This is not easy to integrate  but some software I have gives me the following

length =  √17 + 1/8 log(33 + 1/8 √17)

= 4.647.