a) Work out the value of 5^2-1^5 x 2^4

Answer:

False, since x values cannot have more than one y value.

Step-by-step explanation:

False, since x values cannot have more than one y value.

Answer:

96

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

(2³) (140/7)-32 =128

Answer:

128

Step-by-step explanation:

[2³ ×(140 ÷ 7)] - 32

[2³ ×( 20)] - 32

[8×(20)] - 32

[160] - 32

128

Answer:

25, 25, 22.5, 22

Step-by-step explanation:

It gives you a hint; K = y/x. They give you what x and y are so use that to solve for the last row.

We are given all of these values:

x -> 2, 3, 4, 5

y -> 50, 75, 90, 110

Use the formula given and solve for K.

50/2 = 25

75/3 = 25

90/4 = 22.5

110/5 = 22

Best of Luck!

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer:

Option A, 130°

Hope this helps!

Answer:

164

Step-by-step explanation:

The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively

Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class

The given parameters that will help us to get the percentage are

Mean height of the class = 152 cm

Mean height of the boys = 158 cm

The standard deviation of the boys = 5 cm

Mean height of the girls = 148 cm

Standard deviation of the girls = 4 cm

(1) The percentage of boys in the class is

Total mean height = 158 +148 = 306

Percentage = 158/306 * 100 = 51.6%

Then the  percentages 51.6/100 * 152 = 78%

(2) The total standard deviation of all the students

Boys + girls = 5+4 = 9 cm

Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively

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Answer:

y = x + 2

Step-by-step explanation:

m is the slope (gradient), 12 is the x-coordinate of the point, 14 is the y-coordinate of the point.

y - y1 = m (x - x2)

y - 14 + 1 (x - 12)

y - 14 = x - 12

y = x -12 + 14

y = x + 2

Answer:

5y*5y*5y

Step-by-step explanation:

uhh no explanation cuz logic

The 3rd power of the term 5y without exponents is 125.y.y.y

If a is any positive number and n is its power , then aⁿ means a is multiplied by itself n times

The given term is 5y,

To find the third power of 5y,

The cube of 5y = (5y)³

To write the 3rd power without exponents,

Simplify the term (5y)³.

(5y)³ = 5y x 5y x 5y

       = 125 y.y.y

The required 3rd power of 5y without exponents is 125.y.y.y.

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Answer:

a. 8.95

b. it is

c. yes it belongs

d. males are 2.574 taller than females on average.

Step-by-step explanation:

GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as

a. test statistic = 1.164/0.13

t test = 8.95

b. the regression coefficient of shoe size is 1.164, this is statistically significant

c. Yes the variable shoe size does belong to the model.

d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.

The original number is, if The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number is 52.

An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.

Given:

The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number,

Assume the original number is x then, according to the condition,

10x + 9 + 2x = 633

12x = 633 - 9

x = 624 / 12

x = 52

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Answer:

To locate the number 8 and its opposite on the number line, we can use the given number line:

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Number 8 is located to the right of zero. Its opposite can be found by moving an equal distance to the left of zero. Since the number line is symmetric about zero, the opposite of 8 would be -8.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑ ↑

So, the opposite of 8 is -8. They are related to zero as equal distances on opposite sides of zero on the number line.

Now, let's address exercises 2-3:

a. To locate the opposite of 9, we need to move an equal distance to the left of zero. The opposite of 9 is -9.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

b. To locate the opposite of -2, we need to move an equal distance to the right of zero. The opposite of -2 is 2.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

c. To locate the opposite of 4, we need to move an equal distance to the left of zero. The opposite of 4 is -4.

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

↑

So, the opposites of the given numbers are:

9 → -9

-2 → 2

4 → -4

They are related to zero as equal distances on opposite sides of zero on the number line.

Step-by-step explanation:

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Answer:

Step-by-step explanation:

(-4*5 - 1) + (-4)

(-20 - 1) - 4

-21 - 4

-25

Answer:

it will be 300 feet tall and 1000 feet wide

Step-by-step explanation:

The height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

\(y=ba^x+c\)

Here, a,b and c are the real numbers.

The arch support of a bridge can be modeled by the following function,

\(y=-0.0012x^2+300\)

Here, x and y are measured in feet.

The height and width of the arch has to be found out. First, find the x intercept of the function. As at the x intercept, the y equal to zero. Therefore,

\(0=-0.0012x^2+300\\0.0012x^2=300\\x=\sqrt{25000}\\x=500\)

As, the graph is symmetric around the y-axis. Thus, the -500 can also be a solution. Now, the width of the arch can be given as,

\(w=500-(-500)\\w=1000\rm ft\)

Now similarly at x equal to zero, the function will be,

\(y=300\)

Hence, the height and width of the arch which support of a bridge and modeled by the provided function is 1000 ft and 300 ft long respectively.

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Answer:

the scale factor is 4 to 1, or just 4.

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

4 x 2 x 3 x 4

8 x 12

96

Answer:

a=-1+[(9b)/5]

b=(5/9)+[(5a)/9]

Step-by-step explanation:

The solution for all the parts are given below -

(f + g) (x) = 2x + 3x²

(f - g)(x) = 2x - 3x²

(f . g)(x) = 6x³

( f / g ) (x) = 2x/3x²

A function in mathematics is a relation between dependent variable and an independent variable such that the value of the dependent variable depends upon the existence of the independent one. For example -

f(x) = 3x + 4

f(x) = 2x

Given is f(x) = 2x and g(x) = 3x².

Now, we can evaluate the given expressions as below -

(f + g) (x) = 2x + 3x²

(f - g)(x) = 2x - 3x²

(f . g)(x) = 6x³

( f / g ) (x) = 2x/3x²

Therefore, the solution for all the parts are given below -

(f + g) (x) = 2x + 3x²

(f - g)(x) = 2x - 3x²

(f . g)(x) = 6x³

( f / g ) (x) = 2x/3x²

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Answer:

A) a = 25

B) b = 14

Step-by-step explanation:

hopefully this helps :)

Solve the following:

\( \\ \sf \: a) \: \: \frac{a}{5} + 3 = 8\)

\( \\ \sf \: b) \: \: \frac{3b}{7} - 1 = 5\)

Solving question a) :

\( \\ \sf \frac{a}{5 } + 3 = 8\)

\( \\ \sf \mapsto \frac{a + 15}{5} = 8\)

\( \\ \sf \mapsto \: a + 15 = 8 \times 5\)

\( \\ \sf \mapsto \: a = 40 - 15\)

\( \\ \sf \mapsto \: a = 25\)

\( \\ \sf \therefore \: a = 25\)

Solving question b) :

\( \\ \sf \frac{3b}{7} - 1 = 5\)

\( \\ \sf \mapsto \: \frac{3b - 7}{7} = 5 \)

\( \\ \sf \mapsto3b - 7 = 5 \times 7\)

\( \\ \sf \mapsto3b = 35 + 7\)

\( \\ \sf \mapsto \: b = \frac{42}{3} \)

\( \\ \sf \mapsto \: b = 14\)

\( \\ \sf \therefore \: b = 14\)

a = 25

b = 14

Answer:24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

12+12=24

Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

9514 1404 393

Answer:

  B. -3/4

Step-by-step explanation:

Over the 8-day period from day 2 to day 10, the number of houses sold decreases by 6 from 8 to 2. The average rate of change is ...

  m = houses/day = -6/8 = -3/4

On solving the provided question, we can say that Probability(x>11) = 1 - P(x\(\leq 11\))\ = 0.9645 and Probability(5<x<9) = P(x<9) - P(x<5) = 0.0101 and P(x<9) = 0.0106

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(x>11) = 1 - P(x\(\leq 11\))\

= 0.9645

Probability(5<x<9) = P(x<9) - P(x<5)

= 0.0101

P(x<9) = 0.0106

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