Which equation is equivalent to 3 (x+2) =-7

Answer:

a. True

b. False

c. True

d. False

e. False

Step-by-step explanation:

a. 2.3 + ( -2.3) = 0

b. (-3.7) + (-4.1) = -7.8

c. -2.6 - (-12/4) = 0.4

d. 5/2 + (-2.5) = 0

e. 72 - (-100) = 172

I hope this helps

The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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Answer:

x ≈ 14.7

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan73° = \(\frac{opposite}{adjacent}\) = \(\frac{48}{x}\) ( multiply both sides by x )

x × tan73° = 48 ( divide both sides by tan73° )

x = \(\frac{48}{tan73}\) ≈ 14.7 ( to the nearest tenth )

Answer:

Domain is all real numbers greater than or equal to 7. Range is all real numbers greater than or equal to 9.

Step-by-step explanation:

The domain is possible x-values while the range is possible y-values. This question look like

\( \sqrt{x - 7} + 9\)

The domain of square root function cant have a the radical inside being a negative number because we can't take the sqr root of a negative number and graph it on a cartisean plane We can take the sqr root of 0 . So we set x-7=0. And which x=7 so the domain is all real numbers that are equal to or greater than 7. The range of a sqr root function can only yield any positive y-values. So we must find the lowest point of it. Since the lowest x value we can possible use is 7 we plug it in

\( \sqrt{7- 7} + 9\)

which equals 9. So the range is all real numbers greater than or equal to 9.

Answer:

I think that the short answer will be C) on edge.

Step-by-step explanation:

Edge 2021.

Answer:

y=-2x+5

Step-by-step explanation:

x-2y=2

2y=x-2

y=(x-2)/2

so the slope is 1/2

for lines to be perpendicular m1m2=-1 so the line must have a slope satisfying the condition

(1/2)m=-1

m=-2

the only line with a slope of -2

If is wrong i'm sorry

The equation of the sphere is (x - 6)² + (y - 4)² + (z - 6)² = 6. To find the equation of a sphere, we need the center and the radius of the sphere.

Given the endpoints of one of its diameters, we can determine the center by finding the midpoint, and the radius by finding the distance between the center and one of the endpoints. Let's calculate the center first. The midpoint of the diameter with endpoints (5, 2, 5) and (7, 6, 7) can be found by taking the average of the corresponding coordinates:

Center:

x-coordinate: (5 + 7) / 2 = 6

y-coordinate: (2 + 6) / 2 = 4

z-coordinate: (5 + 7) / 2 = 6

So the center of the sphere is (6, 4, 6).

Next, let's calculate the radius. We can use the distance formula between the center and one of the endpoints:

Radius:

√[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

= √[(7 - 6)² + (6 - 4)² + (7 - 6)²]

= √[1 + 4 + 1]

= √6

The radius of the sphere is √6.

Finally, we can write the equation of the sphere in the standard form:

(x - h)² + (y - k)² + (z - l)² = r²

where (h, k, l) is the center and r is the radius.

Plugging in the values we found:

(x - 6)² + (y - 4)² + (z - 6)² = (√6)²

Simplifying, we have:

(x - 6)² + (y - 4)² + (z - 6)² = 6

Therefore, the equation of the sphere is (x - 6)² + (y - 4)² + (z - 6)² = 6.

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The equatiοn that matches the number of bacteria in the population after 7 hours is \($\begin{array}{l}{{\mathrm{P(t)=Po(4)7}}} \end{array}\). The number of bacteria in the population after 7 hours is 1638400 bacteria.

In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be represented using an equatiοn οr a graph.

We have initial pοpulatiοn 100

it is quadrupled every hοur

\($\mathbf{P}(\mathbf{t})\mathop=\mathbf{P}_{\mathbf{O}}(\mathbf{4})\mathbf{t}$\)

where.

R(t) is population at any time t

Po is initial population

4 is because it is quadruple

t is time in hours

We have tο find after 7 hοurs

\($\begin{array}{l}{{\mathrm{P(t)=Po(4)7}}}\\\\ {{\mathrm{P(t)=100(4)7}}}\end{array}$\)

P(t) = 1638400 bacteria

Thus, equation the matches the number of bacteria in the population after 7 hours is \($\begin{array}{l}{{\mathrm{P(t)=Po(4)7}}} \end{array}\). The number of bacteria in the population after 7 hours is 1638400 bacteria.

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The transformed functions is

a) The absolute value function reflected across the x axis and shifted up 2 units is y₁ = -| x₁ | + 2

b) The absolute value function that is shifted left 3 units and is compressed by a third is y₂ = ( 1/3 ) | x₂ + 3 |

c) The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃ = -5 | x₃ + 4 | + 6

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

a) The absolute value function reflected across the x axis and shifted up 2 units is y₁

The absolute value function is y₁ = | x₁ |

when reflected over x axis , the new function is

y₁ = - | x |

when shifted up 2 units ,

y₁ = -| x₁ | + 2

b)The absolute value function that is shifted left 3 units and is compressed by a third is y₂

The absolute value function is y₂ = | x₂ |

when shifted left 3 units ,

y₂ = | x₂ + 3 |

when compressed by a third , the new function is

y₂ = ( 1/3 ) | x₂ + 3 |

c)The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃

The absolute value function is y₃ = | x₃ |

when reflected across the x axis ,

y₃ = - | x₃ |

when stretched vertically by 5 units ,

y₃ = - 5 | x₃ |

when shifted 4 units left ,

y₃ = - 5 | x₃ + 4 |

when shifted 6 units up ,

y₃ = -5 | x₃ + 4 | + 6

Hence , the transformation of functions are solved

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Answer:

-4z

Step-by-step explanation:

Hi student! Let me help you out.

_____________________

Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us \(\mathrm{-4z}\).

\(\mathrm{-3z-z=-4z}\). -4z is our final answer.

Hope that this helped you! have a good day ahead.

Best Wishes!

\(\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. AIm high. Dream big.}}}}}\bigstar\star\)

◈◈-Greetings!-◆◆

___________________

Answer:

-4z

Step-by-step explanation:

-3z-z

On combining like terms,

= -4z

The company made 900 widgets in one hour

3,600 widgets in 4 hours

therefore 3,600 / 4 for one hour = 900 widgets

900 widgets in one hour.

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Step-by-step explanation:

1)  Total rectangle area =  W x H = 12 x 8 = 96 cm^2

 area of triangle (shaded portion) = 1/2 base * height = 1/2 * 7 x 8 = 28 cm^2

              Nonshaded portion = 96 - 28 cm^2 = 68 cm^2

          ratio shaded:nonshaded is then   28 : 68 = 7:17

2)   Look at the two middle triangles :  Height of each = 8 cm

       then reading across the diagram  height + base + height = 21 cm

            so base = 5 cm

   area of ONE triangle = 1/2 * base * height = 1/2 * 5 * 8 = 20 cm^2

        total area for FOUR of them  = 80 cm^2

Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well. Therefore, the correct answers are options A, B and D.

For each participant in many research, we measure more than one variable. For instance, we track rainfall and plant growth, the quantity of eggs and nesting environment, the number of young, and soil erosion and water volume. Instead of analysing each variable independently (univariate data), we collect pairs of data and try to come up with ways to characterize bivariate data, which involves measuring two variables on each individual in our sample. We start by looking for a correlation between these two variables using the data at hand.

Numerous different kinds of associations between two variables can be found using a scatterplot.

Therefore, the correct answers are options A, B and D.

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Answer:

30

Step-by-step explanation:

20+2((3)(7)−(4)(4))

=20+2(21−(4)(4))

=20+2(21−16)

=20+(2)(5)

=20+10

=30

The unit rate for 96 kilometers in 3 hours  is 32 kilometer per hour.

What is unit rate?

A unit is one of a particular object. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Given in the question,

96 kilometer in 3 hours,

In order to find unit rate we have to change given values in kilometers per hour.

Do, 96 kilometer = 3 hours

96/3 kilometer = 1 hour

Therefore, unit rate is 32 kilometer per hour.

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Te lateral edge lengths of the two similar triangular prisms, and then squaring it, we have determined that the ratio of their surface areas is approximately 5.62:1.

We have two similar triangular prisms with lateral edge lengths of 27 meters and 64 meters. Let's find the ratio of their surface areas.

Step 1: Find the scale factor.
To determine the scale factor between the two prisms, divide the larger lateral edge length (64 meters) by the smaller one (27 meters).

Scale factor = 64 / 27 ≈ 2.37

Step 2: Find the ratio of surface areas.
Since the prisms are similar, their surface areas will be proportional to the square of the scale factor. So, we need to square the scale factor to find the ratio of their surface areas.

Ratio of surface areas = (Scale factor)² = (2.37)² ≈ 5.62

Therefore, the ratio of the surface areas of the two similar triangular prisms is approximately 5.62:1. This means that the surface area of the larger prism is approximately 5.62 times larger than the surface area of the smaller prism.

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The equation -x + y = 5 can be represented in the y = mx + b form as y = x + 5. This form allows us to easily identify the slope and y-intercept of the line represented by the equation.

To express the equation -x + y = 5 in the y = mx + b form, we need to isolate y on one side of the equation.

Starting with -x + y = 5, we can rearrange the equation by moving the -x term to the other side:

y = x + 5

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the coefficient of x is 1, which gives us a slope of m = 1. This means that for every unit increase in x, y will increase by 1. The positive slope indicates that the line will slant upward as we move from left to right.

The constant term in the equation is 5, which gives us the y-intercept, b = 5. The y-intercept is the value of y when x is 0, which in this case is the point (0, 5) on the y-axis.

In the y = mx + b form, the equation -x + y = 5 can be written as y = x + 5. We can quickly determine the slope and y-intercept of the line that the equation represents using this method.

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Answer:

AB

I hope this helps you

:)

The steps in determining the area of the shaded part of a circle include;

The area of the sector is found by multiplying the area of the circle and the ratio of the angle subtended (measure of the central angle) by the sector to 360.

1) The formula for area of a sector of a circle is;

A = (θ/360) * πr²

where πr² is area of circle

θ is the angle subtended by the sector

Thus, we conclude that the area of the sector is found by multiplying the area of the circle and the ratio of the angle subtended (measure of the central angle) by the sector to 360.

2) The area of the triangle formed as part of the segment is subtracted from from the area of the sector.

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The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

The measure of angle x is 40°.

What is geometry?

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and properties of objects in two-dimensional and three-dimensional spaces.

Based on the given information, we can determine the measure of angle x by setting up an equation using the properties of vertical angles and angles on a straight line.

Vertical angles are pairs of angles that are opposite to each other when two lines intersect. They are always congruent, meaning they have the same measure.

In this case, angle y and angle x are vertical angles, so we can set up the equation:

y = x (Vertical angles are congruent)

Angle y forms a straight line with the 80° angle and the 60° angle. The sum of angles on a straight line is always 180°.

So, we can set up another equation for the sum of the angles on the straight line:

80 + 60 + x = 180 (Sum of angles on a straight line is 180°)

Now, we can solve the system of equations by substituting y = x into the second equation:

80 + 60 + y = 180

140 + y = 180

y = 180 - 140

y = 40

Since y = x, we can also determine that x = 40.

Hence, the measure of angle x is 40°.

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Answer:

The answer would be B

Step-by-step explanation:

From 1 second to 3 seconds Denise had stopped

We can tell that this is true because looking at the graph we can see that from 1 to 3 seconds the distance stayed the same which indicates that Denise was not walking

Answer:

I think it is B  between 1 and 3 bc a flat line shows no progress and the only area where is show a flat line is between 1 and 3 so he stopped walking at that point

Step-by-step explanation:

Answer:

A) 15

Step-by-step explanation:

a = 3   b = 5  c = 7

a + b + c

3 + 5 + 7 = 15

Answer:

I believe it is A 15

Step-by-step explanation:

There are 504 different ways the medals can be awarded to the nine competitors.

To find the number of ways the medals can be awarded, we can use the permutation formula:
nPr = n! / (n-r)!
where n is the total number of competitors and r is the number of medals to be awarded (in this case, r=3).
Plugging in the values, we get:
9P3 = 9! / (9-3)!
    = 9! / 6!
    = (9 x 8 x 7 x 6!) / 6!
    = 9 x 8 x 7
    = 504
Therefore, there are 504 different ways the medals can be awarded to the nine competitors. In this situation with nine gymnasts competing for first, second, and third place medals, you can use the concept of permutations. A permutation is an arrangement of objects in a specific order. There are 9 options for the first-place medal, 8 options remaining for the second-place medal, and 7 options remaining for the third-place medal. To find the total number of different ways to award the medals, simply multiply the available options for each position:
9 (first place) × 8 (second place) × 7 (third place) = 504
So, there are 504 different ways to award the first, second, and third place medals to the nine competitors.

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Answer: D Paige

Step-by-step explanation:

Took the test

The employee who experienced the single greatest decline in sales between two months is Paige.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

A graph titled Sales has a month on the x-axis and sales (dollars times 1,000) on the y-axis.

Mary: Starts at 6.4 and ends at 8.6.

Lewis starts at 5.5 and ends at 6.9.

Todd: Starts at 4.6 and ends at 3.3.

Paige: Starts at 7.1 and ends at 7.1.

The difference between the start sales and end sales represents the greatest decline.

Here, Paige has the least difference.

The employee who experienced the single greatest decline in sales between two months is Paige.

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Answer:

Step-by-step explanation:

Ab + ac

Answer:

not a right triangle

Step-by-step explanation:

Using the converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = 12 and 12² = 144

7² + 10² = 49 + 100 = 149 ≠ 144

Then triangle is not right

Answer:

time in years = 2.5 years

Step-by-step explanation:

time = interest / (principal amount x rate)

time = 750 / 5000 x 0.06

time = 750 / 300

time = 2.5 years

Salma must score 405 on exam B in order to do equivalently well as she did on exam A.

To determine how well Salma must score on exam B to perform equivalently to exam A, we need to compare the scores relative to their respective means and standard deviations. Since the scores on each exam are normally distributed, we can use z-scores to make the comparison.

First, we calculate the z-score for Salma's score on exam A using the formula: z = (x - mean) / standard deviation.

For exam A:

z = (69 - 64) / 10 = 0.5

Next, we find the corresponding raw score on exam B that corresponds to the same z-score of 0.5. Using the formula: x = z * standard deviation + mean.

For exam B:

x = 0.5 * 100 + 400 = 405

Therefore, Salma must score 405 on exam B in order to perform equivalently to her score of 69 on exam A. This means that if she achieves a score of 405 on exam B, it would be at the same relative position in the distribution as her score of 69 on exam A, taking into account the different means and standard deviations of the two exams.

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Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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The x-component of fluid acceleration in terms of x and y is 2.

To find the x-component of fluid acceleration (ax), we need to differentiate the x-component of velocity (u) with respect to time.

However, the given equations provide the expressions for u in terms of x and y, not time. Therefore, we need to differentiate u with respect to x and y instead.

Given: u = 2x + y^2

To find the x-component of fluid acceleration (ax), we differentiate u with respect to x while treating y as a constant:

ax = ∂u/∂x = ∂(2x + y^2)/∂x = 2

The x-component of fluid acceleration, ax, is simply 2.

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