What is the area of rectangle ABCD given the information below?

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

In this question, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Answer:

by using distance formula

d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

by putting the values of coordinates

[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]

[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]

[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]

[tex]d=\sqrt{6.25+100}[/tex]

[tex]d=\sqrt{106.25}[/tex]

[tex]d=10.3[/tex]

Step-by-step explanation:

i hope this will help you :)

Answer:

Do you have an image because I'm a bit confused with you just asking the measure of PSQ.

Step-by-step explanation:

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

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

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer:

The original digit is 62

Step-by-step explanation:

Let the Tens be represented with T

Let the Units be represented with U

Given:

Unknown Two digit number

Required:

Determine the number

Since, it's a two digit number, then the number can be represented as;

[tex]T * 10 + U[/tex]

From the first sentence, we have that;

[tex]T = 4 + U[/tex]

[tex]T = 4+U[/tex]

Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]

So;

[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]

[tex]10U + T + 10T + U= 88[/tex]

Collect Like Terms

[tex]10U + U + T + 10T = 88[/tex]

[tex]11U + 11T = 88[/tex]

Divide through by 11

[tex]U + T = 8[/tex]

Recall that [tex]T = 4+U[/tex]

[tex]U + T = 8[/tex] becomes

[tex]U + 4 + U = 8[/tex]

Collect like terms

[tex]U + U = 8 - 4[/tex]

[tex]2U = 4[/tex]

Divide both sides by 2

[tex]U = 2[/tex]

Substitute 2 for U in [tex]T = 4+U[/tex]

[tex]T = 4 + 2[/tex]

[tex]T = 6[/tex]

Recall that the original digit is [tex]T * 10 + U[/tex]

Substitute 6 for T and 2 for U

[tex]T * 10 + U[/tex]

[tex]6 * 10 + 2[/tex]

[tex]60 + 2[/tex]

[tex]62[/tex]

Hence, the original digit is 62

Answer:

12am

Step-by-step explanation:

Answer:

12:00 am or midnight

Step-by-step explanation:

00 00 hrs in 12-hours clock is 12:00 am or 12:00 o'clock midnight.

Answer:

7

Step-by-step explanation:

This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time

Of one of the equal side is 7 than the other one too must be 7

Answer:

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Step-by-step explanation:

Explanation:-

Given data Z = -2 and Z =2

The probability that

P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)

                   = 0.5 + A(2) - ( 0.5 - A(-2))

                  = A (2) + A(-2)

                 = 2 × A(2)     (∵ A(-2) = A(2)

                = 2×0.4772

              = 0.9544

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

Answer:

  [tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]

Step-by-step explanation:

It usually works to factor the denominators, so you can determine the least common denominator.

  [tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]

Answer:

a) 16xy³

Step-by-step explanation:

For a binomial expansion (a + b)ⁿ, the r+1 term is:

nCr aⁿ⁻ʳ bʳ

Here, a = 4x, b = y, and n = 4.

For the fourth term, r = 3.

₄C₃ (4x)⁴⁻³ (y)³

4 (4x) (y)³

16xy³

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

Learn more about domain of a function here

https://brainly.com/question/13113489

#SPJ2

Answer:

1/7

Step-by-step explanation:

There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7

Answer:

1/7

Step-by-step explanation:

The number from the list that is less than 2 is 1.

1 number out of a total of 7 numbers.

= 1/7

Answer:

B. [tex]4^2[/tex]

Step-by-step explanation:

[tex]4^7 \times 4^{-5}[/tex]

Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]

[tex]4^{7 + -5}[/tex]

Add exponents.

[tex]=4^2[/tex]

Answer:

Step by step explanation

[tex] {4}^{7} \times {4}^{ - 5} [/tex]

Use product law of indices

i.e

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] = {4}^{7 + ( - 5)} [/tex]

[tex] = {4}^{7 - 5} [/tex]

[tex] = {4}^{2} [/tex]

Hope this helps...

Best regards!

Answer:

i think this person answered but idrk perseusharrison79

Step-by-step explanation:

For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.

Not drawn to scale

StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction

StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction

StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction

One-half = StartFraction 6 over x EndFraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can calculate this confidence interval using the population proportion calculation. To do this we must find p' and q'

Where p' = 14/100= 0.14 (no of left handed sample promotion)

q' = 1-p' = 1-0.14= 0.86

Since the requested confidence level is CL = 0.98, then α = 1 – CL = 1 – 0.98 = 0.02/2= 0.01, z (0.01) = 2.326

Using p' - z alpha √(p'q'/n) for the lower interval - 0.14-2.326√(0.14*0.86/100)

= -2.186√0.00325

= -2.186*0.057

= 12.46%

Using p' + z alpha √(p'q'/n)

0.14+2.326√(0.14*0.86/100)

= 0.466*0.057

= 26.5%

Thus we estimate with 98% confidence that between 12% and 27% of all Americans are left handed.

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

a) The sample mean is M=200.

The sample standard deviation is s=13.19.

b) Right-tailed. The null and alternative hypothesis are:

[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]

c) At a significance level of 0.01, there is  notenough evidence to support the claim that the arrival rate is significantly higher than 195.

Step-by-step explanation:

We start by calculating the sample and standard deviation.

The sample size is n=30.

The sample mean is M=200.

The sample standard deviation is s=13.19.

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]

This is a hypothesis test for the population mean.

The claim is that the arrival rate is significantly higher than 195.  As we are interested in only the higher tail for a significant effect, this is a right-tailed test.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]

The significance level is 0.01.

The standard deviation of the population is known and has a value of σ=13.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.107)=0.018[/tex]

As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is  notenough evidence to support the claim that the arrival rate is significantly higher than 195.

Answer:

2 hours and 24 minutes

Step-by-step explanation:

2 hours at 60 km/h means you have travelled 2*60=120 km

120 km at 50 km/h takes 120/50 = 2.4 hours

2.4 hours is 2 hours and 0.4*60 = 24 minutes.

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 0.02

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Answer:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Answer:

  5 feet

Step-by-step explanation:

"Twice as tall" means "2 times as tall".

  2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft

The child's mother is 5 feet tall.

Answer:

The mother is 5ft tall

Step-by-step explanation:

2 1/2 + 2 1/2 = 5ft

2ft+2ft = 4ft

1/2+1/2= 1ft

4ft+1ft = 5ft

I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

(C) 4,5,8

Step-by-step explanation:

Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.

Answer:

Option C { 4,5,8 }

Step-by-step explanation:

By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.

* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.

______

{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.

______

Solution = { 4,5,8 }

Answer:

-7

Step-by-step explanation:

4 + (−3 − 8)

PEMDAS

Parentheses first

4 + (-11)

Add and subtract next

-7

Answer:

first I'm using BODMAS

4+(-11)

= -7

hope it helps

Answer:

38500lbs

Step-by-step explanation:

2000 lbs is one tone

if we have 19.25 tons, we need to multiply 19.25x2000

The answer is 38500 lb

Answer:

38,500 pounds

Step-by-step explanation:

Every ton is 2,000 pounds.

We want to find out how many pounds are in 19.25 tons.

Set up a proportion.

pounds/tons=pounds/tons

2,000 pounds/ 1 ton= x pounds / 19.25 tons

2,000/1= x  /19.25

x is being divided by 19.25. The inverse of division is multiplication. Multiply both sides by 19.25.

19.25*2,000/1= x/19.25 *19.25

19.25*2000=x

38,500=x

There are 38,500 pounds in 19.25 tons.