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Find the sum of the first 5 terms of the geometric series. 8 – 16 + 32 – ... 87
86
88
89

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

[tex]Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\[/tex]

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!

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

Answer:

8

Step-by-step explanation:

Because it is equal to the 4 side

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

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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:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Answer:

5! = 120

Step-by-step explanation:

5! is basically 5(4)(3)(2)(1).

Answer:

x = 3 or x = -5

Step-by-step explanation:

x² + 2x - 15 = 0

Factor left side of equation.

(x - 3)(x + 5) = 0

Set factors equal to 0

x - 3 = 0

x = 3

x + 5 = 0

x = -5

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

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:

look up the basic rules for sin and cos

Step-by-step explanation:

Answer:

  9 and 18

Step-by-step explanation:

The numbers are in the ratio 1 : 2, so the ratio of the smaller to the total is ...

  1 : (1+2) = 1 : 3

1/3 of 27 is 9, the value of the smaller number. The larger number is double this, so is 18.

The numbers are 9 and 18.

Answer:

9 and 18

Step-by-step explanation:

you know the explanation since another guy put it

Answer:

a) The length of the building that should border the dog run to give the maximum area = 25feet

b)    The maximum area of the dog run  = 1250 s q feet²

Step-by-step explanation:

Step(i):-

Given function

                       A(x) = x (100-2x)

                      A (x) = 100x - 2x²...(i)

Differentiating equation (i) with respective to 'x'

             [tex]\frac{dA}{dx} = 100 (1) - 2 (2x)[/tex]

     ⇒    [tex]\frac{dA}{dx} = 100 - 4 x[/tex]      ...(ii)

Equating  zero

         ⇒ 100 - 4x =0

         ⇒  100 = 4x

Dividing '4' on both sides , we get

             x = 25

Step(ii):-

Again differentiating equation (ii) with respective to 'x' , we get

    [tex]\frac{d^{2} A}{dx^{2} } = -4 (1) < 0[/tex]

Therefore The maximum value at x = 25

The length of the building that should border the dog run to give the maximum area = 25

Step(iii)

  Given  A (x) = x ( 100 -2 x)

substitute  'x' = 25 feet

             A(x) = 25 ( 100 - 2(25))

                    = 25(50)

                   = 1250

Conclusion:-

   The maximum area of the dog run  = 12 50  s q feet²

Answer:

D

Step-by-step explanation:

The numbers that are less than 0 are negative. Negative numbers have the "-" sign in front of them so the answer is D.

Answer:

d

Step-by-step explanation:

The other ones will always be positive four

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%

Answer:

11.70% probability that the mean height for the sample is greater than 64 inches

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.

In this question:

[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]

What is the probability that the mean height for the sample is greater than 64 inches?

This is 1 subtracted by the pvalue of Z when X = 64.

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

By the Central Limit Theorem

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

[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]

[tex]Z = 1.19[/tex]

[tex]Z = 1.19[/tex] has a pvalue of 0.8830

1 - 0.8830 = 0.1170

11.70% probability that the mean height for the sample is greater than 64 inches

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:

2/3

Step-by-step explanation:

There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.

Answer:

Step-by-step explanation:

This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.

Answer:

see below

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

4x - 3y = 12

Solve for y

Subtract 4x from each side

4x-4x - 3y =-4x+ 12

-3y = -4x+12

Divide by -3

-3y/-3 = -4x/-3 + 12/-3

y = 4/3x -4

The slope is 4/3 and the y intercept is -4

The slope is Positive

Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

[tex]t_{(16 , 0.05)} = 2.1199[/tex]

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )[/tex]

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)

Answer:

x=5  x=-3

Step-by-step explanation:

x^2 − 2x − 15 =0

Factor

What two numbers multiply to -15 and add to -2

-5*3 = -15

-5+3 =-2

(x-5) (x+3)=0

Using the zero product property

x-5 =0   x+3 =0

x=5  x=-3

Answer:

x^2 - 2x - 15 = 0

(x - 5) (x + 3) = 0

x - 5 = 0

x = 5

x + 3 = 0

x = -3

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:

a) Mean of X = 0.40

Variance of X = 0.24

b) Y is a Bernoulli's distribution. Check Explanation for reasons.

c) Mean of Y = 0.80 points

Variance of Y = 0.96

Step-by-step explanation:

a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.

Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.

The probability mass function of X is then

X | Probability of X

0 | 0.60

1 | 0.40

The mean is given in terms of the expected value, which is expressed as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40

Variance = Var(X) = Σx²p − μ²

μ = mean = E(X) = 0.40

Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40

Variance = Var(X) = 0.40 - 0.40² = 0.24

b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.

A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).

Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.

The probability mass function for Y is then

Y | Probability of Y

0 | 0.60

2 | 0.40

c) Mean and Variance of Y

Mean = E(Y)

E(Y) = Σ yᵢpᵢ

yᵢ = each variable

pᵢ = probability of each variable

E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points

Variance = Var(Y) = Σy²p − μ²

μ = mean = E(Y) = 0.80

Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60

Variance = Var(Y) = 1.60 - 0.80² = 0.96

Hope this Helps!!!

Answer:

Sides:

Angles:

Step-by-step explanation:

Apply the law of sines to find the sine of [tex]\angle A[/tex]:

[tex]\displaystyle \frac{\sin{A}}{\sin{C}} = \frac{a}{c}[/tex].

[tex]\displaystyle\sin A = \frac{a}{c} \cdot \sin{C} = \frac{103}{159} \times \left(\sin{104^{\circ}}\right) \approx 0.628556[/tex].

Therefore:

[tex]\angle A = \displaystyle\arcsin (\sin A) \approx \arcsin(0.628556) \approx 38.9^\circ[/tex].

The three internal angles of a triangle should add up to [tex]180^\circ[/tex]. In other words:

[tex]\angle A + \angle B + \angle C = 180^\circ[/tex].

The measures of both [tex]\angle A[/tex] and [tex]\angle C[/tex] are now available. Therefore:

[tex]\angle B = 180^\circ - \angle A - \angle C \approx 37.1^\circ[/tex].

Apply the law of sines (again) to find the length of side [tex]b[/tex]:

[tex]\displaystyle\frac{b}{c} = \frac{\sin \angle B}{\sin \angle C}[/tex].

[tex]\displaystyle b = c \cdot \left(\frac{\sin \angle B}{\sin \angle C}\right) \approx 159\times \frac{\sin \left(37.1^\circ\right)}{\sin\left(104^\circ\right)} \approx 98.8[/tex].

Answer:

x < 5 or x > 1

Step-by-step explanation:

2x - 6 < 4

2x < 4 + 6

2x < 10

x < 10/2

x < 5

2x - 6 > - 4

2x > - 4 + 6

2x > 2

x > 2/2

x > 1

Answer:

She makes conclusion about a population that is not well represented by the sample.

Step-by-step explanation:

The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.

The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.

Answer: The sample is biased

Answer:

The sampled populations have equal variances

Step-by-step explanation:

ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.

Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.

Question Correction

One common system for computing a grade point average​ (GPA) assigns 4 points to an​ A, 3 points to a​ B, 2 points to a​ C, 1 point to a​ D, and 0 points to an F. What is the GPA of a student who gets an A in a 3​-credit ​course, a B in each of three 4​-credit ​courses, a C in a 2​-credit ​course, and a D in a 3​-credit ​course?

Answer:

2.75

Step-by-step explanation:

We present the information in the table below.

[tex]\left|\begin{array}{c|c|c|c}$Course Grade&$Grade Point(x)&$Course Credit(y)&$Product(xy)\\---&---&---&---\\A&4&3&12\\B&3&4&12\\B&3&4&12\\B&3&4&12\\C&2&2&4\\D&1&3&3\\---&---&---&---\\$Total&&20&55\end{array}\right|[/tex]

Therefore, the GPA of the student is:

[tex]GPA=\dfrac{55}{20}\\\\ =2.75[/tex]

Answer:

The answer is

Step-by-step explanation:

For an nth term in an arithmetic sequence

[tex]U(n) = a + (n - 1)d[/tex]

where n is the number of terms

a is the first term

d is the common difference

From the question

a = 15

d = 24 - 15 = 9

n = 61

So the 61st term of the arithmetic sequence is

U(61) = 15 + (61-1)9

= 15 + 9(60)

= 15 + 540

= 555

Hope this helps you.