What is the RANGE of the cluster shown on this graph?

1 - 9 seconds


0 - 14 meters


1 - 6 meters


1 - 3 seconds

The number of sugar cups will be equal to 7.5 cups.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.

The number of sugar cups will be calculated as,

F / S = 2 / 3

5 / S = 2 / 3

S = ( 5 x 3 ) / 2

S = 7.5 cups

Therefore, the number of sugar cups will be equal to 7.5 cups.

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There is no sufficient evidence to support that the population mean is less than 165.

What is mean ?

The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.

From the given data

183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158

Mean = 157.5833

Standard deviation s = 24.39

  n = 12

Null hypothesis  [tex]H_{0}[/tex] : μ = 165

Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165

Level of significance ∝ = 0.05

degree of freedom (df) = n - 1

                                (df) = 12 - 1

                                (df) = 11

critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)

Test - statistics (t) = ( mean - μ ) / ( s / √n)

                         (t) = -1.053

p - value = 0.1574

p - value > Significance level (∝)

 0.1574 > 0.05

We fail to reject the null hypothesis

Critical value [tex]t_{0.05 , 11}[/tex] = -1.796

                   |[tex]t_{0.05 , 11}[/tex]| = 1.796

|test - statistics| < |critical value|

1.053 < 1.796

We fail to reject the null hypothesis

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When a  bi-athlete travels 50 km in 2 1/6 hours . cycling part of the way at 30 km/h and running the rest at 12 km/h. the athlete ran 10 km

we generate two equations from the concept of speed =  distance / time

let the time for cycling be x and time for running be y

therefore

x + y = 2 1/6 hours

distance for cycling

= 30 * x

= 30x

distance for running

= 12 * y

= 12y

total distance

30x + 12y = 50

solving the equation simultaneously

30x + 12y = 50

x + y = 2 1/6

x = 4/3 and y = 5/6

How far the bi-athlete run

= 12y

= 12 * 5/6

= 10 km

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Answer:

x=-10

Step-by-step explanation:

-3x-7=-8x-57

Add 8x: 5x-7=-57

Add 7: 5x=-50

Divide 5: x=-10

The example of a complex fraction is the fraction that consisting fraction on the numerator or denominator or both, that is 4 / (1/6)

The simple fraction consist of both numerator and denominator as whole number. The term on the top is the numerator and the term on the bottom is called the denominator

The complex fraction is defined as the fraction that consisting fraction on the numerator or denominator or both

The example of the complex fractions are

4 / (1/6)

Here the numerator is the 4 and it is a whole number. The denominator is 1/6 that is a fraction

Therefore, the example of a complex fraction is 4 / (1/6)

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Answer:

$300

Step-by-step explanation:

S = amount of $$ Shivani currently has

Y = ... Yamini currently has

1. If Shivani gives 60 to Yamini, the amounts with both will be equal:
   S - 60 = Y + 60

2. if Yamini gives 20 to Shivani, the amount with Shivani would become twice the amount left with Yamini: 2(Y-20) = S+20

3. Simplify both equations and solve the system:

   S = Y + 120
   S = 2Y - 60

   Y + 120 = 2Y - 60  ⇒  Y = 180

   S = 180 + 120 = 300

Answer:

31

Step-by-step explanation:

Because c = -9 and d = -5, we replace the variables in the expression with the corresponding numbers.

cd + c + d --- >  (-9)(-5) + (-9) + (-5)

Then we solve it.

(-9)(-5) + (-9) + (-5)

   45 + (-9) + (-5)

        36 + (-5)

             31

The degree of the term is the power of the term

The degree of a phrase with a single variable is the exponent of that variable. The degree is equal to the exponents of all the variables when there are many variables.

degree we find by just looking at its power.

To further understand the word, let's look at an example.

[tex]7x^{8}[/tex] degree is 8

[tex]6y^{2}[/tex]degree is 2,

[tex]x^{2}[/tex] +[tex]y^{5}[/tex] degree will be 7

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The balance of an account is given as follows:

[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]

The meaning of each parameter is given as follows:

The payments in this problem are given as follows:

For the balance over 20 years, the values of the parameters are given as follows:

P = 135, r = 0.035, n = 12, t = 20.

Then the balance is given as follows:

[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]

[tex]B = \frac{135\left(\left(1 + \frac{0.035}{12}\right)^{12 \times 20}-1\right)}{\frac{0.035}{12}}[/tex]

B = $93,113.

The contributed amounts are given as follows:

Hence the accrued interest is of:

93,113 - (21,600 + 10,800) = $60,713.

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The value of x in the considered inequality's solution set is given by -10.

What is  inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

We have;

3(x - 4) ≥ 5x + 2

By solving;
3(x - 4) ≥ 5x + 2

3x - 12 ≥ 5x + 2

Adding -3x-2 on both sides we get ;

-12-2 ≥ 5x-3x

-14 ≥ 2x

Dividing both sides by 2,we get;

-14/2 ≥ 2x/2

-7 ≥ x

x ≤ -7

As a result, any numbers that are less than or equal to -7 comprise the solution set for this inequality.

There is currently only the value -10 in the solution set because -10 ≤ -7.

As a result, the value of x in the collection of solutions to the inequality under consideration is provided by -10.

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21⁰

sin0=opp/hyp

sin0=5/14

0=(sin^-1)5/14

0=21⁰

Answer:

Inequality: 40x + 13100 ≤ 24500

x ≤ 285

Step-by-step explanation:

Answer:

y = -194x + 3850

Step-by-step explanation:

slope intercept form

y = mx + b

info from question:
. slope = -194

. five years later same school has 3850 students

Hope this helps!

- vo

The mean number of goals the team scored is 2.3

Mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency. To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of values.

Basically, the mean of a data set is the average of the entire data

mean = sum of all data / total number of data

mean = 23 / 10

mean = 2.3

The mean is 2.3

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The equation that represents how many grams of the compound will remain after 4 hours is A(4) = 380 *(1 - 12.1%)⁴

From the question, we have the following parametersa:

Mass = 380 grams

Rate of decay= 12.1% per hour

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of hours = 4

A  = Initial mass = 380

r = rate of decay = 12.1%

Substitute the known values in the above equation, so, we have the following representation

A(4) = 380 *(1 - 12.1%)⁴

Hence, the equation is A(4) = 380 *(1 - 12.1%)⁴

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The confidence interval for the population proportion p is: 0.3031, 0.4367.

First step is to find the population proportion p

p= x/n

p = 52/141

p = 0.37

Second step is to find the margin of error

z-score for 95 % confidence interval is 1.645

Margin of error = 1.645√0.37 (1- 0.37)/141

Margin of error = 1.645√0.37 (0.63)/141

Margin of error = 1.645√0.00165319

Margin of error = 1.645(0.04065945)

Margin of error = 0.06688

Third step is to find the Confidence interval

Confidence interval = p ± MOE

Confidence interval = (0.37 - 0.06688) , (0.37 + 0.06688)

Confidence interval =0.3031, 0.4367

Therefore the Confidence interval is 0.3031, 0.4367.

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When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The two triangles are congruent if we can demonstrate that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.

Triangles are considered congruent by SAS if their two sides match those of the other triangle's corresponding two sides, and if their included angles are parallel in both triangles.

Hence we get the required answer.

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The amount they earn from the sale of candy canes as required is; $6.75.

It follows from the task content that the amount earned by Raven and Tyler as in the task content is to be determined.

Since they sell their cups of hot chocolate for $2.25 in which case they sold 11 cups.

However, the question requires that the amount which they earn from the sale of candy canes is to be determined.

Therefore, since each candy cane is sold for $0.75, it follows that the amount earned on 9 candy cones is;

= 9 × $0.75

= $6.75

Ultimately, the amount earned from the candy canes is; $6.75.

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The expression that represents the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

It is important to note that an expression simply refers to mathematical statements which have at least two terms which are then related by an operator. In this case, they contain either numbers, variables, or both.

In this case, since Hayden rode his bike 5 times and each time he biked a 3 mile path, a 2 mile path, and a 2 1/4 mile path. Then in this situation, the expression will be:

= 5 × (3 + 3 + 2 1/4)

In conclusion, the correct option is A.

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0.01023 is the probability of obtaining a success

Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:

P(X = r) = nCr . p^r  . q^n-r

Given: number of trial (n) = 17, probability of success (p) = 0.6, X=15

probability of failure (q) = 1 - 0.6 = 0.4

P(X = 15) = 17C15 × 0.6¹⁵ × 0.4¹⁷⁻¹⁵

P(X = 15) = 17C15 × 0.6¹⁵ × 0.4²

P(X = 15) = 136 × 0.6¹⁵ × 0.16

P(X = 15)  = 0.01023

Therefore, the probability of obtaining a success is 0.01023

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If triangle RST is an acute triangle, then m∠S must be less than 90°.

What is Acute Traingle?

A form of triangle called an acute triangle has acute angles at each of its three internal angles. Triangles with sharp angles are also known as acute triangles. Acute triangles have different side lengths, but their interior angles are always less than 90°.

In light of the foregoing, if triangle RST is an acute triangle,

then,

∠R , ∠S and ∠T, all are less than 90.

A triangle that is equilateral and has all three interior angles equal and less than 90 degrees, or angles that are all 60 degrees, is an example of an acute triangle.

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By using Unitary method it can be calculated that

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

 1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

a) Here, Unitary method will be used

Blue Paint                   White Paint

(Quart)                          (Quart)

[tex]1\frac{1}{2}[/tex]                                     5

[tex]1\frac{1}{5}[/tex]                                     4

1                                        [tex]3\frac{1}{3}[/tex]

5 quarts of white paint is mixed with [tex]\frac{3}{2}[/tex] quarts of  blue paint

1 quart of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5} \times 4[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{6}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

Again

[tex]\frac{3}{2}[/tex] quarts of blue paint is mixed with 5 quarts of white paint

1 quart of blue paint is mixed with  [tex]5 \div \frac{3}{2}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]\frac{10}{3}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

c) Finally

  4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

   1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

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Answer: C) 15/2

Step-by-step explanation:

Using the formula for the sum of an infinite geometric series,

[tex]\frac{5}{1-\frac{1}{3}}=\frac{15}{2}[/tex]

The slope of the line that passes through (2,4) , (9,10) is 6/7

From the question, the points are given as

(2,4) , (9,10)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (2,4) and (9,10)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2,4) and (9,10)

Substitute the known values in the above equation

So, we have the following equation

Slope = (10 - 4)/(9 - 2)

Evaluate

Slope = 6/7

Hence, the slope of the line is 6/7

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Answer:

  (√2/2)(sin(x) +cos(x))

Step-by-step explanation:

You want sin(x+π/4) written in terms of sine and cosine.

The sine of the sum of two angles is found using the identity ...

  sin(α +β) = sin(α)cos(β) +cos(α)sin(β)

Choosing α=x and β=π/4, this becomes ...

  sin(x +π/4) = sin(x)cos(π/4) +cos(x)sin(π/4)

The trig function values are ...

  sin(π/4) = cos(π/4) = √2/2, so the expression can be written ...

  sin(x +π/4) = sin(x)√2/2 +cos(x)√2/2

  sin(x +π/4) = (√2/2)(sin(x) +cos(x))

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The standard form of the complex numbers ( 7 − 5 i ) ⁢ ( 2 + 3 i ) is

Complex numbers are numbers that are represented of the form a + ib

a and b are real numbers. a is the real part and b is in the imaginary part

i = √-1

Opening up the parenthesis by multiplication  

( 7 − 5 i ) ⁢ ( 2 + 3 i )

= 14 +21i - 10i -15i^2

where i^2 = -1

= 14 +21i - 10i -15 * -1

= 14 +21i - 10i +15

= 29 + 11i

The equation is equal to 29 + 11i

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