Fill in the blank to make the fractions equivalent.

Answer:

Step-by-step explanation:

1. it is reflected along the y=x

2. is reflected along x=-4

3. reflected along y=x

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{15}=\cfrac{15}{25}\implies \cfrac{x}{15}=\cfrac{3}{5}\implies 5x=45\implies x=\cfrac{45}{5}\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{25=y+x}\implies 25=y+9\implies \boxed{16=y} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{z}=\cfrac{z}{y}\implies \cfrac{25}{z}=\cfrac{z}{16}\implies 400=z^2\implies \sqrt{200}=z\implies \boxed{20=z}[/tex]

Answer:

7/5

Hope this helps...

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7/5

multiplicative inverse means the number which when multiplied to the given number the product is one.

The length and width of the new rectangular field are 82.5 meters and 82.5 meters, respectively.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we need to understand the relationship between perimeter, area, length, and width of a rectangle.

The perimeter of a rectangle is the sum of all four sides, which is calculated as P = 2(L + W), where L is the length and W is the width of the rectangle. In this case, the perimeter of the given rectangular field is:

P = 2(L + W) = 2(105 + 60) = 330 meters

Now, we know that the new rectangular field also has the same perimeter of 330 meters, but a larger area. The formula for the area of a rectangle is A = L x W, where L is the length and W is the width of the rectangle.

Let's assume the length and width of the new rectangular field are L₁ and W₁, respectively. We need to find the values of L₁ and W₁ that satisfy the following two conditions:

The perimeter of the new rectangular field is 330 meters.

The area of the new rectangular field is greater than the area of the given rectangular field.

We can use the first condition to solve for L₁ in terms of W₁:

P = 2(L₁ + W₁) = 330

L₁ + W₁ = 165

L₁ = 165 - W₁

We can substitute this expression for L₁ into the formula for the area of the rectangle to get:

A₁ = L₁ x W₁ = (165 - W₁) x W₁ = 165W₁ - W₁^2

To find the maximum value of A₁, we can take the derivative of the above expression with respect to W₁ and set it equal to zero:

dA₁/dW₁ = 165 - 2W₁ = 0

W₁ = 82.5

Substituting this value of W₁ back into the expression for L₁, we get:

L₁ = 82.5

This rectangle has the same perimeter as the given rectangular field, but a larger area.

In summary, we can find the length and width of another rectangular field that has the same perimeter but a larger area by setting up equations for the perimeter and area of the new rectangle, solving for one variable in terms of the other, and then finding the maximum value of the area by taking the derivative of the area equation with respect to one of the variables.

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Tommy who tosses 3 coins, the probability that he tosses two tails specify that he has tossed at least one tail is equals to the 0.428.

Probability is chance of occurrence of an event. It is calculated by the number of favourable outcomes divided by total number of possible outcomes. Tommy tosses 3 coins, total number of possible outcomes on tossing = 8

Here, we can define, two events

A : tossing two tails in three coin flips.

B : tossing at least one tail in three coin flips

Now we want to determine P(A|B) . The number of possible favourable outcomes for getting two tails = 3

The probability of occurrence of an event A, P( A) = [tex]\frac{3}{8} [/tex]

Probability of occurrence of event B, P(B) = [tex]\frac{7}{8} [/tex].

P(B|A) : denotes if two tails in three flips, the coin has definitely turned up tails at least once. Therefore this probability is equals to 1 .Using Baye's theorem,

P(A/B) = [tex]\frac{ P(A)⋅P(B|A)}{P(B)} [/tex]

= [tex]\frac{ \frac{ 3}{8} ×1}{\frac{7}{8}} [/tex]

= 0.428

Hence, required probability is 0.428.

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The height of the pyramid is 10 units.

We have,

The formula for the volume of a triangular pyramid is V = (1/3)Bh,

where B is the area of the base and h is the height of the pyramid.

The base of the pyramid is a triangle with a base of 12 units and a height of 6 units, so its area is:

B = (1/2) x base x height

   = (1/2) x 12 x 6 = 36 square units.

We know that the volume of the pyramid is 120 cubic units, so we can plug in the values for B and V in the formula and solve for h:

V = (1/3) x B x h

120 = (1/3) * 36 * h

120 = 12h

h = 10 units

Therefore,

The height of the pyramid is 10 units.

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A triangular pyramid is a geometrical shape which has a triangular base and three triangular faces. It has a vertex common to all the three lateral faces of a triangular pyramid. The height of the pyramid is 10 units.

A volume is simply defined as the amount of space occupied by any three dimensional solid. These solids can be a cube, cuboid, a cylinder or a sphere. It is generally measured in cubic units.

The equation used to calculate volume is:

V = (1/3)B

Base area:

B = (1/2) x base x height

= (1/2) x 12 x 6 = 36 square units

Volume:

V = (1/3) x B x h

120 = (1/3) * 36 * h

120 = 12h

h = 10 units

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The length of the third wire piece is [tex]7 / 20 m[/tex].

A length means the measurement or extent of something from end to end. It is the measure of distance from Point A to Point B.

Given:

First piece length = 3/20 m

The second piece length is:

= (5/3) x (3/20) m

= 1/4 m

The total length of the first two pieces is:

= 3/20 m + 1/4 m

= 2/5 m

The length of the third piece will be:

= Total length - Length of first two pieces

= 3/4 m - 2/5 m

= (15 - 8) /20

= 7/20 m.

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Answer:

b > -8

Step-by-step explanation:

Given inequality:

[tex]4b-3(2b-6) > 3-(5b+9)[/tex]

To solve for b, begin by expanding the brackets on the left side of the inequality:

[tex]4b-3 \cdot 2b -3 \cdot (-6) > 3-(5b+9)[/tex]

[tex]4b-6b +18 > 3-(5b+9)[/tex]

Distribute the negative sign inside the parentheses on the right side:

[tex]4b-6b +18 > 3-5b-9[/tex]

Combine like terms on both sides of the inequality:

[tex]-2b +18 > -5b-6[/tex]

Add 5b to both sides:

[tex]-2b +18 +5b > -5b-6+5b[/tex]

[tex]3b+18 > -6[/tex]

Subtract 18 from both sides:

[tex]3b+18-18 > -6-18[/tex]

[tex]3b > -24[/tex]

Divide both sides by 3 to isolate b:

[tex]\dfrac{3b}{3} > \dfrac{-24}{3}[/tex]

[tex]b > -8[/tex]

Therefore, the solution to the given inequality is:

[tex]\large\boxed{\boxed{b > -8}}[/tex]

After matching the given angles to their values, the results are:

In the given unit circle we have the angle details and the value associated with that angle. From the given unit circle,

From the above analysis, we can match the given details.

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Quadratic equation models the data which is y = -3[tex]x^{2}[/tex] - 9x + 3.

To find the function that models the data, we need to analyze the pattern of the values of x and y.

As we observe the values of y, we notice that they decrease in a non-linear way as x increases. Moreover, the values of x are equally spaced, with a difference of 1 between each consecutive value.

Thus, we can deduce that the function that models this data is a quadratic function of the form y = a[tex]x^{2}[/tex] + bx + c. To find the coefficients a, b, and c, we can substitute the values of x and y from the table into the equation and solve for the coefficients.

Using the method of least squares, we can calculate the coefficients as follows:

a = -3

b = -9

c = 3

Therefore, the quadratic function that models the data is:

y = -3[tex]x^{2}[/tex] - 9x + 3.

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The only option that describes the given histogram is; D.) Numerical and univariate.

A histogram is defined as a graphical representation representing data points that are organized into user-specified ranges.

Now, we see that from the given histogram that it shows how much water is used in a household in a given day.

Since it is dealing with amount of water, then we can call this a numerical data set since it is only one and doesn't categorize anything.

Secondly, since it gives only one information which is the amount of water for each household, then we can call this a univariate data set.

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complete question:

The display shows how much water is used in a household in a given day. Which of the following describes this data set

A.) Categorical and bivariate

B.) Categorical and univariate

C.) Numerical and bivariate

D.) Numerical and univariate

Answer:

An angle that has a measure between 90 and 180 degrees is called an obtuse angle. An obtuse angle is characterized by having a measure greater than 90 degrees but less than 180 degrees. In other words, the angle "opens up" more than a right angle (which has a measure of 90 degrees) but less than a straight angle (which has a measure of 180 degrees).                                                                             Obtuse

Step-by-step explanation:

brain

Answer:

The answer is 0.7

Step-by-step explanation:

steve=2/5of hard disk program

remaining space=1-2/5=3/5

shella=1/3 of hard disk programs

remaining space =1-1/3=2/3

remaining space if steven deletes one program taking 1/10

=remaining space+1/10

R=3/5+1/10=7/10

The exact scaled dimensions of the room is: 81 inches by 60 inches

First, we convert 27 ft. and 20 ft. to inches to make it easier to work with. This would convert like this:

27 ft. x 12 in. = 324 in.

20 ft. x 12 in. = 240 in.

This also means that the scale converts to 1/4 in. = 12 in.

Now, take the 324 in. and 240 in. and apply them to the scale.

For every 12 in. (1 ft.) in the non-scale room dimensions, there will be one 1/4 in. on the scale. That would apply like this:

324 in. (27 ft.) * 1/4 in. = 81 in. [or 6.75 ft.]

240 in. (20 ft.) * 1/4 in. = 60 in. [or 5 ft.]

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Answer:

Unfortunately, you have not provided any information about the functions M and P, so I cannot determine which statement about their rates of change is true.

Please provide more context or details about the functions M and P so that I can assist you better.

The function change if the base of the exponent were between 0 and 1 is  y = a * 0.5^x.

Function is a type of relation, or rule, that maps one input to specific single output.

We are given that the exponent must be greater than 1;

If the base of the exponent were 1, then the function would not change at all. This is because any number raised to the power of 1 is itself. For example, y = a * 1^x would simplify to y = a, which is a horizontal line.

If the base of the exponent were between 0 and 1, then the function would change from growth to decay. This is because as x increases, b^x decreases. For example, y = a * 0.5^x would show a decreasing pattern as x increases. This is called an exponential decay function.

Therefore, by the function the answer will be y = a * 0.5^x.

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Based on the sample data, we can say that kids collected less candy this year compared to the average of 83 pieces.

Null hypothesis: The true population means of candy collected by kids on Halloween is 83.

Alternative hypothesis: The true population means of candy collected by kids on Halloween is less than 83.

We will use a significance level of 0.05.

Using a one-sample t-test with the following formula:

t = (x - μ) / (s / √n)

Here x is the sample mean, μ is the hypothesized population mean (83), s is the sample standard deviation, and n is the sample size.

t = (69 - 83) / (5.2 / √150) = -7.27

Using a t-distribution table with degrees of freedom equal to 149 (since we have 150 observations in the sample), we find that the p-value is less than 0.0001.

Since the p-value is less than the significance level of 0.05.

So, reject the null hypothesis and conclude that the true population means of candy collected by kids on Halloween is less than 83.

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The exact values of sin(θ), cos(θ), and tan(θ) are -4/5, -3/5 and 4/3 respectively.

The exact values of sin(θ), cos(θ), and tan(θ) is calculated as follows;

sec(θ) = 1/cos(θ)

1/cos(θ) = -5/3

cos(θ) = -3/5

The value of sin (θ) is calculated as follows;

sin²(θ) + cos²(θ) = 1

sin²(θ) + (-3/5)² = 1

sin²(θ) + 9/25 = 1

sin²(θ) = 1 - 9/25

sin²(θ) = 16/25

sin(θ) = ±√(16/25)

sin(θ) = - 4/5

The value of tan(θ) is calculated as follows;

tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-4/5)/(-3/5)

tan(θ)   = 4/3

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"If Elenor earns $85 weekly, how much money will she deposit each week if she deposits 20% of her earnings into a savings account?"

If Elenor earns $85 weekly, she will deposit 20% of that amount into her savings account. To find out how much money she will deposit each week, we can use the following steps:

Calculate 20% of $85 by multiplying $85 by 0.20 (which is the same as dividing $85 by 5):

20% of $85 = $85 x 0.20 = $17

Therefore, Elenor will deposit $17 into her savings account each week.

So, Elenor will deposit $17 each week into her savings account.

The side length of the square is 22.36 units.

For a square of side length S, the area is given by the square of the side length, so we can write:

V = S²

In this particular case, we know that the area is 500 square units, then we can replace that in the above formula to get:

500 = S²

Solving this for S, we will get.

√500  =S

22.36= S

The side length is 22.36 units.

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It is recommended to consume a pre-competition meal consisting of an egg white sandwich with 2 egg whites and 2 pieces of white bread about 3-4 hours before the competition. This allows enough time for digestion and absorption of nutrients, while also preventing any discomfort or bloating during the event.

An explanation for this timing is that it takes around 3-4 hours for a meal to pass through the stomach and into the small intestine, where most of the nutrient absorption occurs.

Consuming a meal too close to the competition may cause digestive issues or an energy crash, while consuming it too far in advance may result in hunger or a drop in blood sugar levels.

In summary, timing is important when it comes to consuming a pre-competition meal. It is recommended to consume an egg white sandwich with 2 egg whites and 2 pieces of white bread about 3-4 hours before the competition to allow for proper digestion and absorption of nutrients, while also preventing discomfort or energy crashes during the event.

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Answer:

2.6

Step-by-step explanation:

13/5 is 2.6

I hope i am right but if not then i am so sorry

The distance between the medic and the shelter is 626.3 feet.

A helicopter was hovering over a shelter and was 900 ft above the ground. A medic was on the ground and was looking up at an angle of 55 degrees to the helicopter.

The medic’s eyes were 5.5 feet off the ground when looking at this right angle of elevation.

This situation forms a right angle triangle. Therefore, the distance of the medic to the shelter can be found as follows:

Hence,

tan 55 = opposite / adjacent

tan 55 = 900 - 5.5 / a

cross multiply

a tan 55° = 894.5

divide both sides by tan 55°

a =  894.5 / 1.42814800674

a = 626.335645885

a = 626.3 feet

Hence,

distance between medic and shelter = 626.3 feet

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Samuel is correct that the system of equations -6x - 6y = -6 and 7x + 7y = 7 have infinitely many solutions since the ratio of the coefficients of x, y, and constants all are equal.

The system of equations are:

-6x - 6y = -6

7x + 7y = 7

Hayden says the solution is (1, 1) so this must satisfy both the equations.

For (1, 1),

-6x - 6y = -6*1 - 6*1 = -6 - 6 = -12 ≠ -6

So the value does not satisfy the first equal so this cannot be the solution.

Hence Hayden is incorrect.

We know that the system of equations ax + by = c and dx + ey = f have infinitely many solutions if a/d = b/e = c/f.

Here a = -6, b = -6, c = -6, d = 7, e = 7, f = 7

a/d = -6/7

b/e = -6/7

c/f = -6/7

Here a/d = b/e = c/f so the system of equations -6x - 6y = -6 and 7x + 7y = 7 have infinitely many solutions.

Hence Samuel is correct.

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Answer: 2/3

Step-by-step explanation: d/dy (y^n) =ny^n -1

Hopes this helps you I try

It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a 'Multiple Testing' problem. The one-way ANOVA controls for the Type I Error and should be used instead. Comparing multiple pairs of means using independent two-sample t-tests without adjusting for the multiple comparisons can lead to an increased probability of committing a Type I error.

When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, it is appropriate to use a one-way ANOVA instead of multiple independent two-sample t-tests. The reason is that performing multiple t-tests increases the overall Type I error rate, which is the probability of falsely rejecting a true null hypothesis. This is known as the multiple testing problem, and it occurs when we conduct multiple hypothesis tests without controlling the overall error rate.

In contrast, the one-way ANOVA controls for the Type I error rate and tests the null hypothesis that all population means are equal. If the null hypothesis is rejected, then at least one population mean is significantly different from the others. We can then perform post-hoc tests, such as Tukey's HSD, to determine which population means are different.

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The special name for the result obtained when taking the given information and forming a z-score in a hypothesis test for the mean is the test statistic.

When you take the given information and form a z-score in a hypothesis test for the mean, the special name of that result is called the "test statistic."

This value helps determine the likelihood of observing the sample mean, given the null hypothesis is true, and is used to make a decision regarding the hypothesis.

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If side of square is (x-1) units, and the dimensions of rectangle are x units by (x-2) units, then

(a) the possible values are : all real number greater than 2,

(b) Square has a greater area than rectangle,

(c) The difference in area is 1 unit.

Part (a) : To be a valid square, the sides must have the same length. So, we equate expression for length of each side of square equal to each other and solve for x:

x - 1 = x - 1

0 = 0

This equation is true for any value of x, so the possible values of x are all real numbers.

To be a valid rectangle, the length and width must both be positive.

So, we equate the expressions for the length and width of the rectangle greater than 0 and solve for x:

x > 0 and x - 2 > 0

x > 2,

Therefore, the possible values of x are all real-numbers greater than 2.

Part(b) :

The side of square is = (x-1),

So, it's area is represented by : (x-1)² = x² - 2x + 1;

The rectangle's length is : (x) units,

The rectangle's width is : (x-2) units,

So, the area will be = x(x-2) = x² - 2x,

We see that, the area of the square has a greater area than the rectangle,

Part (c) :

The difference in both areas will be calculated as : Area of Square - Area of rectangle;

(x² - 2x + 1) - (x² - 2x) = 1 units.

Therefore, the difference is 1 units.

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The given question is incomplete, the complete question is

A square has sides that are (x-1) units long and a rectangle has a length of x units and a width of (x-2) units;

(a) What are the possible values of x?

(b) does the square or the rectangle have the greater area?

(c) What is the difference in the areas?