Triangle XYZ, XY= 80, ZY= 64 XZ= 48 what is the cosine

Answer:

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Step-by-step explanation:

Proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

This means that the null hypothesis is:

\(H_0: p = 0.11\)

And the alternate hypothesis is:

\(H_a: p > 0.11\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.11 is tested at the null hypothesis:

This means that \(\mu = 0.11, \sigma = \sqrt{0.11*0.89}\)

Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent.

This means that:

\(n = 1550, X = \frac{214}{1550} = 0.1381\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.1381 - 0.11}{\frac{\sqrt{0.11*0.89}}{\sqrt{1550}}}\)

\(z = 3.54\)

Pvalue of the test and decision:

This is the probability of finding a sample proportion above 0.1381, which is 1 subtracted by the pvalue of Z = 3.54.

\(z = 3.54\) has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:

Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:

(x^3 - 12x^2) + (-2x + 24)

Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:

x^2(x - 12) - 2(x - 12)

Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:

(x - 12)(x^2 - 2)

Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).

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Answer:

A certain shade of pink us created by adding 3 cups of red paint to 7 cups of white paint

Step-by-step explanation:

Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

To make color pink,

for every 3 cups of red , we need 7 cups of white.

Let 'r' be the cups of red required

let 'w' be the cups of white required

so , as per the question

for 3 r we need = 7 w

r = 7/3 w

so, 7/3 is constant of proportionality

Answer:

The resultant of the given vectors by component method is \(\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km]\).

Step-by-step explanation:

First we define each vector by applying using rectangular form:

1) \(\|\vec E\| = 23\,km\), 11º north of east.

\(\vec E = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})\) (Eq. 1)

2) \(\|\vec N\| = 25\,km\), 24º east of north.

\(\vec N = 25\,km\cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})\) (Eq. 2)

3) \(\|\vec G\| = 19\,km\), 18º south of west.

\(\vec G = 19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})\) (Eq. 3)

4) \(\|\vec R\| = 27\,km\), 58º west of north.

\(\vec R = 27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})\) (Eq. 4)

The resultant of given vectors is determined by vector sum, that is:

\(\vec U = \vec E + \vec N + \vec G + \vec R\) (Eq. 5)

\(\vec U = 23\,km\cdot (\cos 11^{\circ}\,\hat{i}+\sin 11^{\circ}\,\hat{j})+25\,km \cdot (\sin 24^{\circ}\,\hat{i}+\cos 24^{\circ}\,\hat{j})+19\,km\cdot (-\cos 18^{\circ}\,\hat{i}-\sin 18^{\circ}\,\hat{j})+27\,km\cdot (-\sin 58^{\circ}\,\hat{i}+\cos 58^{\circ}\,\hat{j})\)

\(\vec U = (23\,km\cdot \cos 11^{\circ}+25\,km\cdot \sin 24^{\circ}-19\,km\cdot \cos 18^{\circ}-27\,km\cdot \sin 58^{\circ})\,\hat{i}+(23\,km\cdot \sin 11^{\circ}+25\,km\cdot \cos 24^{\circ}-19\,km\cdot \sin 18^{\circ}+27\,km\cdot \cos 58^{\circ})\,\hat{j}\)

\(\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km]\)

The resultant of the given vectors by component method is \(\vec U = -8.222\,\hat{i}+35.664\,\hat{j}\,\,\,[km]\).

Answer:

(-1,5)

Step-by-step explanation:

Answer:

Tan<C=2.4

Step-by-step explanation:

Opp=36

Adj=15

Tan<C=opp/adj

Tan<C=36/15

Tan<C=2.4

Hope this helps :) ❤

The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

(A)

As per the given,

Principle amount P = $7,000

Rate of interest r = 3.2%

Number of times interest applied per time period n = 4 (Quarterly)

(B)

Time period T = 7 year

Total amount S(7) = 7,000(1 + 0.032/4)^(4 x 7)

S(7) = $8749.6954

Hence "The value of P = $7,000,r = 3.2%, n = 4, and money after 7 years will be $8749.6954".

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Answer:

the answer is the last one

Answer:

No solution

Step-by-step explanation:

4(x-8) = 4x-8

Distribute.

4x-32 = 4x-8

Subtract 4x first and get rid of the variable (x).

4x-32 = 4x-8

-4x        -4x

-32 = -8

-32 does not equal -8, so there is no solution!

Have an amazing day!! c:

Answer:

I think the answer is 8

Step-by-step explanation:

t h e   a n s w e r   i s    8   b c    f o r    e v e r y  1  b o o k   i t s   8$

40   d i v i d e d    b y    5   i s  8

 h o p e   t h i s   h e l p s :)

Answer:

It was ready at 2:30 pm :)

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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What's your numerator and denominator value?

Answer:

The lowest score on the final exam that would qualify a student for an​ A is 80.

The lowest score on the final exam that would qualify a student for a B is 74.68.

The lowest score on the final exam that would qualify a student for a C is 67.33.

The lowest score on the final exam that would qualify a student for a​ D is 62.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 71 and a standard deviation of 7.

This means that \(\mu = 71, \sigma = 7\)

Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's.

This means that:

90th percentile and above: A

70th percentile and below 90th: B

30th percentile to the 70th percentile: C

10th percentile to the 30th: D

Lowest score for an A:

Top 10% receive A, which means that the lowest score that would qualify a student for an A is the 100 - 10 = 90th percentile, which is X when Z has a pvalue of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 71}{7}\)

\(X - 71 = 7*1.28\)

\(X = 80\)

The lowest score on the final exam that would qualify a student for an​ A is 80.

Lowest score for a B:

70th percentile, which is X when Z has a pvalue of 0.7, so X when Z = 0.525.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.525 = \frac{X - 71}{7}\)

\(X - 71 = 7*0.525\)

\(X = 74.68\)

The lowest score on the final exam that would qualify a student for a B is 74.68.

Lowest score for a C:

30th percentile, which is X when Z has a pvalue of 0.3, so X when Z = -0.525.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.525 = \frac{X - 71}{7}\)

\(X - 71 = 7*(-0.525)\)

\(X = 67.33\)

The lowest score on the final exam that would qualify a student for a C is 67.33.

Lowest score for a D:

10th percentile, which is X when Z has a pvalue of 0.1, so X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.28 = \frac{X - 71}{7}\)

\(X - 71 = 7*(-1.28)\)

\(X = 62\)

The lowest score on the final exam that would qualify a student for a​ D is 62.

In order to find the slope between those two points, we can use the following formula for the slope:

Where m is the slope between the points (x1, y1) and (x2, y2).

So using the points (-4, 2) and (5, 6), we have:

So the slope is 4/9

Answer:

(29.46 mm, 29.54 mm).

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 43 - 1 = 42

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 42 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.018

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.018\frac{0.12}{\sqrt{43}} = 0.04\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 29.5 mm - 0.04mm = 29.46 mm

The upper end of the interval is the sample mean added to M. So it is 29.5 mm + 0.04mm = 29.54 mm

The 95% confidence level for the true mean width is: (29.46 mm, 29.54 mm).

Answer:

Step-by-step explanation:

A range

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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Answer:

(First answer option)

Step-by-step explanation:

General form of an exponential function

\(y=ab^x+c\)

where:

Given exponential function:

\(y=4(10)^x-3\)

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\(\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}\)

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

An asymptote is a line that the curve gets infinitely close to, but never touches.

The parent function of an exponential function is:

\(f(x)=b^x\)

As x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  \(f(x) = ab^x+c\) always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

A graph representing exponential growth will have a curve that shows an increase in y as x increases.

A graph representing exponential decay will have a curve that shows a decrease in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).  

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

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Answer: C. (5, -1).

Step-by-step explanation:

The measure of the side MN is 19.1.

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The different trigonometric identities are expressed as:

From the information given, we have that:

Using the tangent identity:

\(\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}\)

Substitute the values

\(\text{tan}(60) =\dfrac{\text{MN}}{11}\)

Cross multiply the values, we have:

\(\text{MN} = \sf 1.73(11)\)

\(\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}\)

Hence, the measure of the side MN is 19.1.

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9514 1404 393

Answer:

  no, yes, yes, no, yes

Step-by-step explanation:

You're looking for values greater than -1.5. All positive numbers will be greater than any negative number.

The two negative numbers among the answer choices are both to the left of -1.5 on the number line. They are less than -1.5, so are not greater than -1.5.

The negative numbers are No; the positive numbers are Yes.

Answer:

Roughly 10.30

Step-by-step explanation:

Use Pythagorean theorem:
\(c^2 = a^2 + b^2\)

Where \(c\) is your hypotenuse

So:

\(c^2 = (9)^2 + (5)^2\)

\(c= \sqrt{106}\)

\(c\) ≈ \(10.30\)

Answer:10.3

Step-by-step explanation:

Answer/Step-by-step explanation:

Five more than a number = 5 + n

The sum of 3.6 and a number = n + 3.6

The difference of ten and a number = 10 - n

One-half less than a number = n - (1/2)

I hope this helps!

Answer:

The difference of 10 and a number: 10-n

Five more than a number: 5+n

The sum of 3.6 and a number: n+3.6

one-half less than a number: n-1/2

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

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The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Answer: F

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:

Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.