The temperature in Tampa, Florida, is 15 degrees warmer than twice the temperature in Chicago, Illinois. The temperature in Tampa is 75 degrees. Write an equation to determine
the temperature in Chicago.

987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]

What is scientific notation?

Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.

When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].

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The volume of the triangular prism is 308 in³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, Alfred made a container shaped like a triangular prism,

Given are the dimensions, 14 in., 4 in. and 11 in.

Volume of a triangular prism = BxHxL/2

= 14x4x11/2 = 616/2 = 308 in³

Hence, The volume of the triangular prism is 308 in³

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We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

What do you mean by  Annexation?

International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.

According to the question,

We have the given data:

A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.

The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.

This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.

Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.

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Answer:

j = - 8

Step-by-step explanation:

1 - j/4 - 3

1 is also 4/4

so

4/4 - j/4 = 3

4 - j/ 4= 3

multiply by 4 on both sides

which gets you

-j  + 4 = 12

minus 4 from both sides

-j = 8

j = -8

Answer:j=-8 I hope this helps

Step-by-step explanation:

1-j/4=3

Multiply both sides of the equation by 4

which gives you

4-j=12

Move the constant to the right-hand side and change its sign
-j=12-4

Subtract the numbers

-j=8

Change the signs on both sides of the equation

j=-8 - This is your answer

Answer:

3y, 9y²

Step-by-step explanation:

We use laws of binomial

(a+b)²=a²+2ab+b²

From this, we get

15x × * × 2 = 90xy

2×*=6y

*=3y

Now, we square this term to get the last term

3y×3y=9y²

Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.

A method of determining a function's derivative is differentiation. Mathematicians use the technique of differentiation to determine the instantaneous rate of change in a function based on one of its variables. The most typical example is velocity, which is the rate at which a distance changes in relation to time.

Here,

ΔABC & ΔDBE

=> AC/DE = BC/BE

=> h/6 = 20 /20-x

=> h = 120/20-x

Differentiate w.r.t  to t

=> dh/dt = [tex]\frac{120}{{(20-x)}^{2} }[/tex] * dx/dt

given the man is walking towards wall at the rate of 5 ft/s

thus, dx/dt =5 ft/s

=>dh/dt =  [tex]\frac{120}{{(20-5)}^{2} }[/tex] * 5

=>dh/dt =  8/3 ft /sec

Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.

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Answer:

b = [tex]\sqrt{2p/a}[/tex]

Step-by-step explanation:

The given equation is:

p=1/2ab^2

Multiply by 2 on both sides

2p = ab^2

Then divide by a on both sides,

b^2 = 2p/a

take square root on both sides, then we can get subject of b,

b = [tex]\sqrt{2p/a}[/tex]

Hence, the subject of the given equation make the value of b is b = [tex]\sqrt{2p/a}[/tex]

The subject of an equation is the value that is being solved for. An equation is a mathematical statement consisting of an equality sign (=) between two expressions that have the same value. The expression on the left side of the equality sign is called the left-hand side, while the expression on the right side of the equality sign is called the right-hand side. The left-hand side of the equation can be thought of as what is being solved for, while the right-hand side of the equation can be thought of as the clues or tools that are used to solve for the left-hand side. For example, in the equation 3x + 1 = 7, the subject of the equation is the variable x, which is the value that is being solved for.

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Answer:

Below

Step-by-step explanation:

3x+15      <==== factor out '3'

3 * ( x+5)       done !

Answer:

Step-by-step explanation:

7/8
------
3/10

use the fraction rule: 7x10/8x3- 35/12

try that, im not sure if its fully correct

The required probability of getting exactly 3 heads is 0.3.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total sample space = 2×5 = 10
Favorable outcome (3 heads) = 3
Probability is given of getting exactly 3 heads
= favorable outcome / total sample space

Substitute the value in the above equation
= 3 / 10
= 0.3

Thus, getting the 3 heads while tossing a coin 5 times has a probability of 0.3.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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The length of one piece is equal to 85 inches and the other piece is equal to 107 inches.

The quantity or formula required to change a measurement from one system of units to another is known as a conversion factor. The number is typically presented as a numerical ratio or fraction that can be multiplied.

As from the conversion factor we know that,

1 Feet = 12 Inches

So, 16 Feet = 16 * 12 = 192 inches

Let the length of one piece be x

Then the other piece length will be x + 22

The required equation will be

x + x + 22 = 192

2x = 170

x = 85.

Hence, the length of one piece is equal to 85 inches and the other piece is equal to 107 inches.

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Answer:

x = 3[tex]\sqrt{7- x}[/tex]

Step-by-step explanation:

so what you do here is move the x to the other side.

X^2 = 63 - x

then you square root both sides

so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]

so you end up with

x =   [tex]\sqrt{63 - x}[/tex]

so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with

x = 3[tex]\sqrt{7- x}[/tex]

have a good day :)

Answer:

50x + 9500 ≤ 27500

x ≤ 360

Step-by-step explanation:

50x + 9500 ≤ 27500  Subtract 9500 from both sides

50x + 9500 - 9500 ≤ 27500 - 9500

50x ≤ 18000  Divide both sides by 50

[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]

x ≤ 360

The value of k for the function k f( 3 ) = 7 f( 2 ) is 2

What is a Function ?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given information

We are given with the function

f( x ) = 2 -3x

f ( 3 ) = 2 - 3(3)

        = 2 - 9

f ( 3 ) = -7

f ( 2 ) = 2 - 2(2)

        = 2 - 4

f ( 2 ) = -2

We are given

k f( 3 ) = 7 f( 2 )

k ( -7 ) =  7 ( -2 )

k = 2

The value of k for the function k f( 3 ) = 7 f( 2 ) is 2

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The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. Since it was first described on the first page of Euclid's Elements, the vocabulary for classifying triangles is more than two thousand years old. Modern categorization names are either literal transliterations of Euclid's Greek or their Latin interpretations.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is used to signify a triangle in the previous illustration.

FD/DC=ED/DG

2x+7/48=5x-2/40

40(2x+7)=48(5x-2)

80x+280=240x-96

160x=376

x=2.35

Therefore, The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

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Answer:

a. -4

b. 1/4

Step-by-step explanation:

a. [tex]\textrm{slope}_{||} = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{-4}{1} = -4[/tex]

b. [tex]\textrm{slope}_\perp = \dfrac{-1}{\textrm{slope}_{||}} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]

Answer:

Step-by-step explanation:

g(x) = (-x)1/2

9 square meters is the area of triangle LMN. Using the concept of Heron's formula.

Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.

According to Heron's formula the area = √s (s - a)(s - b)(s - c)

A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.

a triangle with three sides, a, b, and c.

given data was LM = 7,MN = 6 and perimeter was given by 16m

As we know perimeter is the sum of all the sides  

so, Perimeter=LM + MN + NL

NL=Perimeter-(LM+MN)

NL=16 - 7 - 6

NL= 3

By Heron's formula,

Area = √[(s(s-a)(s-b)(s-c)].  

where s = perimeter/2

so, s = 16/2 = 8

area = √[(8(8-7)(8-6)(8-3)]

area = 8.94427191 ≈ 9 square meters.

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Answer: 9m

Step-by-step explanation:

Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

Answer:0.41

Step-by-step explanation:

The value of y in the equation y=x2+2x+5 when x=3 is y= 20

Simplifying algebraic expressions is the same idea, except you have variables (or letters) in your expression.

simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving

y=x^2+2x+5

mathematically, x=3

substitute the valve of x=3 into the equation

y= 3^2 + 2(3) + 5

y= (3x3) + 2(3) +5

Evaluate the value of y by adding the numbers together

y= 9 + 6+ 5

y= 20

Therefore, the value of y in the equation y=x^2+2x+5  is 20

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A proportional relationship is when a change in one variable results in a change in the other variable in a consistent manner.

similar to direct variation in the form

y = k × x

where,

y = dependent variable

x = independent variable

k = constant.

The relationship between how much Steven charges and time is a proportional relationship because the rate of change between the two variables is constant. This can be seen in the equations:

For 3 hours: cost = 15.75

For 5 hours: cost = 26.25

The rate of change can be calculated by dividing the difference in costs (26.25 - 15.75) by the difference in time (5 hours - 3 hours) which equals a rate of 5.50 per hour. This rate remains constant for all other time increments, making it a proportional relationship.

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Answer:

-48y+24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠)

=-6(8y+-4)

=-48y+24

Answer:

-48y + 24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠) =

= −6⁢(⁠8y - 4)

= -48y + 24

The system of inequalities that matches the graph is defined as follows:

The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.

This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:

y ≤ 3x

he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.

When x increased by 3, y decayed by 6, hence the slope of the line is of:

m = -6/3 = -2.

Then:

y = -2x + b.

When x = 1, y = -3, then the intercept is given as follows:

-3 = -2 + b

b = -1.

Thus the constraint is of:

y > –2x – 1.

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