Which expressions are equivalent to the one below? Check all that apply.log(10^7)

Answer:

[tex]\sf P(A \cap B)=\dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Event A - spinning violet or yellow

Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.

[tex]\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}[/tex]

Event B - rolling an even number

Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6.  Therefore, the even numbers are 2, 4 and 6.

[tex]\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]

Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.

For independent events A and B:

[tex]\implies \sf P(A \cap B)=P(A)P(B)[/tex]

To find P(A and B), substitute the found values of P(A) and P(B):

[tex]\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]

P(A)

P(B)

3 even nos are 2,4,6

P(A[tex]\cap[/tex])

Answer:

[tex]\sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Explanation:

[tex]\rightarrow \sf \dfrac{3}{4} - \dfrac{1}{5}[/tex]

make the denominators same by lcm

[tex]\rightarrow \sf \dfrac{5(3)}{20} - \dfrac{4(1)}{20}[/tex]

expand the following

[tex]\rightarrow \sf \dfrac{15}{20} - \dfrac{4}{20}[/tex]

Join the fractions together

[tex]\rightarrow \sf \dfrac{15-4}{20}[/tex]

Subtract the integers

[tex]\rightarrow \sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Answer:

11/20 or 0 whole 11/20 or 0.55

Step-by-step explanation:

Find the least common multiple (LCM) of 4 and 5 at first:

We can't do the LCM of 5 and 4,so just multiply them, 5*4 = 20

Now,

For 3/4 : divide 20 by 4,then multiply the result by 3.For 1/5 : divide 20 by 4, then multiply the result by 1. Simple!

Subtracting the numerators,

As a whole number:

As a decimal:

Answer:

x = $1 & y = $2.

Each doughnut cost $1 and hot chocolate cost $2.

The multiplicative rate of change is 2/3

The complete question is in the image

The multiplicative rate of change is then calculated as:

r = y2/y1

This gives

r = 4/6

Simplify

r = 2/3

Hence, the multiplicative rate of change is 2/3

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Answer:

b.

Step-by-step explanation:

Answer:

g

Step-by-step explanation:

for this function, we put in the value of "g" (because it is the cause of the function--it is the independent variable [it changes; and it doesn't rely on something else to change] )

so, because the part independently changing is the gas used, that is our input of this graph.

(you can imagine this to be a graph, which typically has the independent variable that we are directly changing--x--along the x-axis, which is where we would place g.)

hope this helps!!

The value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have two functions:

f(x) = 1 - x²

g(x) = √(11 - 4x)

f(-1) = 0

g(-1) = √15

f(2) = -3

g(2) = √3

(f/g)(-1) = f(-1)/g(-1) = 0/√15  = 0

(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3

(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15

(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3

Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is  -3√3, the value of (g - f)(-1)  is √15, and the value of (g + f) (2) is √3 - 3

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Answer: D, $116

Step-by-step explanation:

A = 100(1 + 0.03)^5

A = 100(1.03)^5

A = 100(1.1593)

A = 115.92

Hope this helped!

The parabola with the minimum at (4, -3) is the third option:

[tex]y = 0.5*x^2 - 4x + 5[/tex]

Remember that for a parabola of the form:

[tex]y = a*x^2 + b*x + c[/tex]

If a > 0, the minimum is at the x-value of the vertex:

[tex]x = \frac{-b}{2a}[/tex]

If a < 0, there is no minimum (so we discard option 2).

Taking the third option:

[tex]y = 0.5*x^2 - 4x + 5[/tex]

The x-value of the vertex is:

[tex]x = \frac{-(-4)}{2*0.5} = 4[/tex]

As expected.

To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.

[tex]y = 0.5*(4)^2 - 4*4 + 5 = -3[/tex]

So the minimum is at (4, -3), as expected, so that is the correct option.

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Answer: it is the median

Step-by-step explanation:

Answer:

it is the Mode,Median,and Mean.

Step-by-step explanation:

There are ALWAYS three measures of the “center"

The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.

We can draw the above situation as a form of a right-angle triangle.

From the figure, the distance between AB is x ft

From the right angle triangle DBC:

tan66 = 122/CB

CB = 54.31 ft

From the right angle triangle DAC

tan16 = 122/AC

AC = 425.46 ft

x = AC - CB

x = 425.46 - 54.31

x = 371.15 ft ≈ 371 ft

Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

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Answer: 63 and 17 differ by 46.

Step-by-step explanation:

63-17=46

Subtraction is what you do when trying to find the difference of something.

Answer:

in triangle ACD and BCE

AC = EC

angle ACD = angle ECB ( COMMON ANGLE).

CB = CD

BY side and side criteria

triangle ACD is congruent to triangle BCE

so angle a is congruent to angle E

hence, proved

Option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

As we know the line of best is represented by:

y = mx + c

Here m is the slope and c is the y-intercept.

A scatter plot is made to model the amount of money left to pay on a mortgage.

Every month that passes, the amount left to pay decreases.

Plug x = 0 to get the y-intercept

y = c

The y-intercept representing the original amount of the mortgage.

Thus, option third "The original amount of the mortgage" is correct because every month that passes, the amount left to pay decreases.

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Answer:

d) 5.88×10^9

Step-by-step explanation:

Answer:

d) 5.88 × 10⁻⁹

Explanation:

[tex]\rightarrow \sf \left(1.2\cdot 10^7\right)\left(4.9\cdot 10^2\right)[/tex]

[tex]\sf apply \ exponent \ rule : a^b + a^c = a^{b + c}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7}\cdot \:10^{2}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^{7+2}[/tex]

[tex]\rightarrow \sf 1.2\cdot \:4.9\cdot \:10^9[/tex]

[tex]\rightarrow \sf 5.88 \cdot \:10^9[/tex]

The number of people in the sample survey is 75.

Survey sampling, as used in statistics, is the process of choosing a sample of constituents from a target population to perform a survey. The word "survey" can be used to describe a wide range of observational methods or procedures. Most frequently, a questionnaire meant to assess people's traits and/or opinions is employed in survey sampling. The topic of survey data collecting involves various methods of contacting sample participants after they have been chosen. Sampling is done to cut down on the expense and/or labor required to survey the complete target population. A census is a survey that includes all members of the target population. A sample is a subset or segment of a population from which data will be drawn.

The sample survey has

5 people in 1-4 miles per week

10 people in 5-8 miles per week

15 people in 9-12 miles per week

20 people in 13-15 miles per week

25 people in 16-19 miles per week

The number of people in the sample survey is

5 + 10 + 15 + 20 + 25

=5(1 + 2 + 3 + 4 + 5)

=5(15)

=75

Hence, the number of people in the sample survey is 75.

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Answer:

  2

Step-by-step explanation:

Corresponding sides are proportional in these similar triangles.

__

  short side/long side = k/4 = 4/8

  k = 4(4/8) . . . . multiply by 4

  k = 2

_____

Additional comment

The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...

  l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN

  l = 2√5

  m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN

  m = 4√5

The similarity statements are ...

  ΔLMN ~ ΔLNO ~ ΔNMO

The function that represents how much you would pay is:

p(x) = (x - $5)*0.9

Let's say that the cost of the repair is x.

First, we apply the coupon, so we discount $5 for the cost.

x - $5.

Then we apply another discount of the 10%, this is written as:

(x - $5)*(1 - 10%/100%)

(x - $5)*(1 - 0.1)

(x - $5)*0.9

Then the function that represents how much you would pay is:

p(x) = (x - $5)*0.9

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The standards that use 2.4 GHz are:

A wifi standard defines two characteristics of the wi-fi network, which are speed and frequency.

Such that there are two common frequencies, 2.4 GHz (usually with larger speed) and 5 GHz (usually with lower speed)

The standards that use 2.4 GHz are:

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The simplified radical for the given equation is 2√3.

The given equation is [tex]\frac{3}{x} =\frac{x}{4}[/tex].

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

[tex]\frac{3}{x} =\frac{x}{4}[/tex]

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

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Answer:

Let's solve your inequality step-by-step.

−4x+7>x−13

Step 1: Subtract x from both sides.

−4x+7−x>x−13−x

−5x+7>−13

Step 2: Subtract 7 from both sides.

−5x+7−7>−13−7

−5x>−20

Step 3: Divide both sides by -5.

−5x/−5>−20/−5

x<4

Answer:

x<4

IMAGINE AN ARROW ABOVE THE NUMBERS

⇔

−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7

4 is where the line is circled and the arrow is facing left

←Ф

like that

Answer:

x<4

Step-by-step explanation:

So you will put an open circle on positive 4 and a ray going to the left of the graph.

The amount of money earned by Kiki earned $614 in three days.

The amount paid by any company or industry to the employees after deductions of the several taxes is the salary.

Given that:

Per day salary of Kiki = $150

Commission = 8% of sales

Worth of sold items = $350+$500+$1200 = $2050

Amount of commission = 0.08 x 2050 = $164

Total amount earned in three days = Base salary per day * Number of days + Commission

Total amount earned = 150*3 + 164

Total amount earned = 450 + 164 = $614

Hence, Kiki earned $614 in three days.

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Answer:

x=5 1/4 or 5.25

Step-by-step explanation:

11x2-4x=1

22-4x=1

22-1-4x=

21-4x=

21=4x

x=5 1/4 or 5.25

Answer:

Using the formula of quadratic equation, we find x = 0.534 and x = -0.17.

Step-by-step explanation:

It is a quadratic equation.

11x² - 4x - 1 = 0

Find the determinant of the quadratic equation.

D = b² - 4ac

D = 16 + 44

D = 60

One of the values of x will be

x = (-b+√D)/2a

x = (4+2√15)/22

x = 0.534

The second value will be

x = (-b-√D)/2a

x = (4-2√15)/22

x = -0.17

The two values of x, from the quadratic formula are 0.534 and -0.17.

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Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

The equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.

It is defined as a function that is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.

As we know the sin function is represented by:

y = Asin(Bx) + C

Here,

A = The amplitude  =  3

C = The vertical shift  = 1

B - The period in terms of π

B = 2π/amplitude

B = 2π/4

B = π/2

The becomes:  

[tex]\rm y = 3sin(\dfrac{\pi }{2}x)+1[/tex]

Thus, the equation of the sin function is y = 3sin(πx/2) + 1, and the graph of the function is shown in the picture.

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Answer:

[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]

Step-by-step explanation:

Given expression:

[tex](a+b)(a^2-ab+b^2)[/tex]

Using the Distributive Property Law, expand the brackets:

[tex]\implies a(a^2-ab+b^2)+b(a^2-ab+b^2)[/tex]

[tex]\implies a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]

Group like terms:

[tex]\implies a^3+b^3-a^2b+a^2b+ab^2-ab^2[/tex]

As  -a²b+a²b=0  and  ab²-ab²=0  then:

[tex]\implies a^3+b^3[/tex]

Answer:

y = 25°

Step-by-step explanation:

115° and x are a linear pair and sum to 180° , so

x + 115° = 180° ( subtract 115° from both sides )

x = 65°

the sum of the 3 angles in the triangle = 180° , then

x + x + 2y = 180°

65° + 65° + 2y = 180°

130° + 2y = 180° ( subtract 150° from both sides )

2y = 50° ( divide both sides by 2 )

y = 25°

Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

We need to pay attention to what symbols to use.

Solid circle

Empty circle

Arrow

Square brackets: [ and ]

Curved brackets: ( and )

Union of sets: ∪

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     [tex]-4[/tex]

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     [tex]0[/tex]

So, the first part of our range is:

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    [tex]2[/tex]

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    [tex]\infty[/tex]

So, the second part of our range is:

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

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