Find the value of the y when 5y + 45 = 100

The mortar shell will strike the target in 0.02 seconds

The duration to strike the target is solved using the formula for velocity which is

= distance / time

The problem gives the distance to be 3 feet and velocity is 150ft/s

therefore

150 = 3 / time

time = 3 / 150

time = 0.02 seconds

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Answer:

1. The minimum head breadth that will fit the clientele is of 4.41-in.

2. The maximum head breadth that will fit the clientele is of 7.19-in.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 5.8-in and a standard deviation of 0.8-in.

This means that \(\mu = 5.8, \sigma = 0.8\)

1. What is the minimum head breadth that will fit the clientele?

The 4.1st percentile, that is, X when Z has a pvalue of 0.041, so X when Z = -1.74.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.74 = \frac{X - 5.8}{0.8}\)

\(X - 5.8 = -1.74*0.8\)

\(X = 4.41\)

The minimum head breadth that will fit the clientele is of 4.41-in.

2. What is the maximum head breadth that will fit the clientele?

100 - 4.1 = 95.9th percentile, that is, X when Z has a pvalue of 0.959, so X when Z = 1.74.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.74 = \frac{X - 5.8}{0.8}\)

\(X - 5.8 = 1.74*0.8\)

\(X = 7.19\)

The maximum head breadth that will fit the clientele is of 7.19-in.

Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

\( \frac{4x + 1}{6x} \div \frac{x}{3x - 1} \)

\( = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} \)

\( = \frac{(4x + 1)(3x - 1)}{x(6x)} \)

\( = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } \)

\( = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } \)

The inequality that describes the possible value of x is

The triangles described gave the information to form the inequality equation

from the description it can be deduced that

m< bca = m< dce vertical angles

since side 12 is greater than 10 then m< bac > m< dec

therefore 50 > 5x - 10

solving for x

50 > 5x - 10

50 + 10 > 5x

60 > 5x

x < 12

therefore 2 < x < 12 is the inequality that represents x

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The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

\(f(x) = \log_2{x}\)

The translated function is then given as follows:

\(g(x) = \log_2{x + 4} + 8\)

The y-intercept of the function is the numeric value at x = 0, hence:

\(g(0) = \log_2{0 + 4} + 8\)

g(0) = 2 + 8 = 10.

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

45-32 = 13 / 32 *100= 40.625 round to the nearest percent is 41%

Step-by-step explanation: Brainlest plzzz

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Using the concept of critical point and the second derivative test, it is found that the correct option is:

D. f(x) has a relative maximum at x = 3 and a relative minimum at x = 5.

Applying the second derivative test at the critical points, we have that:

In this problem:

The correct option is:

D. f(x) has a relative maximum at x = 3 and a relative minimum at x = 5.

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Answer:

There are 200 1/8's in 25.

Step-by-step explanation:

If I am thinking of this correctly then there are 200. Basically, what how I interpreted this is that you mean 8 1/8's make up 1. and you need 25 whole 1's. If that is the case the correct answer is 200.

200 1/8. Hope this helps and feel better!

Table is attached below-

1) 1 m² = 10.75 tiles

2) 10 m² = 107.5 tiles

3) 9.3 m² of tiles = 100 tiles

4) a m² = 10.5a tiles

We have been given that

Every square meter of ceiling requires 10.75 tiles.

we have find missing values in the table.

We know,

1 square meter of ceiling =  10.75 tiles.      ...(i)

1. Therefore, the number of tiles corresponding to 1 square meter of         ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

2. Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

(1/10.75) square meter of ceiling = 1 tile.

Multiply both sides by 100.

(100/10.75) square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

3. Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling =  a×10.75 tiles.

a square meter of ceiling =  10.75a tiles.

4. Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.

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Answer:

-18 2/3 or -56/3

Step-by-step explanation:

The true statement about the right rectangular prisms include:

It should be noted that a prism simply means a shape that has two identical shapes that face each other.

Here, the angles in the smaller prism measure 90 degrees and the perimeter of the rectangular bases changes by a factor of 2.

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Answer:

1,2, and 5

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

all the details are in the attached picture. The suggested solution is not the shortest way.

Note, step 1 is: to find the domain; step 2 is: to solve the equation wihout domain; step 3: to determine 'x' with domain. The answer is marked with green colour.

Option B. 5 and one-third units. The value of a in triangle XYZ is 5 and two-thirds units. This is found using the Pythagorean theorem twice and solving for a.

To find the value of a, we can use the Pythagorean theorem in triangles WZY and WYX as follows:

In triangle WZY:

\(c^2 = 3^2 + (a + 4)^2\)

In triangle WYX:

\(b^2 = 4^2 + a^2\)

Since angle ZWX is a right angle, we can use the Pythagorean theorem in triangle ZWX as follows:

\(ZWX^2 = ZW^2 + WX^2\)

We know that ZW = c and WX = b, so we have:

\(a^2 + b^2 = c^2\)

Substituting\(c^2\) in terms of a and simplifying, we get:

\(a^2 + b^2 = 25 + (a + 4)^2\)

Expanding and simplifying, we get:

\(a^2 + b^2 = a^2 + 8a + 41\)

Subtracting \(a^2\) from both sides, we get:

\(b^2 = 8a + 41\)

Substituting \(b^2\) in terms of a in the equation \(a^2 + b^2 = c^2\), we get:

\(a^2 + 8a + 41 = c^2\)

Substituting\(c^2\) in terms of a from the equation for triangle WZY, we get:

\(a^2 + 8a + 41 = 9 + (a + 4)^2/16\)

Expanding and simplifying, we get:

\(16a^2 + 128a + 656 = 9a^2 + 50a + 97\)

Simplifying further, we get:

\(7a^2 + 78a - 559 = 0\)

Using the quadratic formula, we get:

\(a = (-78 ± sqrt(78^2 + 4(7)(559))) / 14\)

a = (-78 ± sqrt(49379)) / 14

Since a represents a length in a triangle, it must be positive. Therefore, we have:

a = (sqrt(49379) - 78) / 14 ≈ 6.67

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Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.

What is the value of a?

A. 5 units

B. 5 and one-third units

C. 6 and two-thirds units

D. 7 units

Answer:

a). m∠AED = 70°

b). x = 10°

Step-by-step explanation:

a). Quadrilateral ABDE is a cyclic quadrilateral.

Therefore, by the theorem of cyclic quadrilateral,

Sum of either pair of opposite angle is 180°

m(∠AED) + m(∠ABD) = 180°

m(∠AED) = 180° - 110°

m(∠AED) = 70°

Since, ∠AED ≅ ∠EAD

Therefore, m∠AED = m∠EAD = 70°

b). By triangle sum theorem in ΔABD,

m∠ABD + m∠BDA + m∠DAB = 180°

110° + 40° + m∠DAB = 180°

m∠DAB = 180° - 150°

m∠DAB = 30°

m∠BAE = m∠EAD + m∠BAD

              = 70° + 30° = 100°

By angle sum theorem in ΔACE,

m∠EAC + m∠AEC + m∠ACE = 180°

100° + 70° + x° = 180°

x = 180° - 170°

x = 10°

Answer:

86°

Step-by-step explanation:

try suggested solution (see the attached picture), note, the suggested way is not the shourtest one.

Answer:

5 packages

Step-by-step explanation:

each would have five if they made 5 sandwhiches

Answer:

5

Step-by-step explanation:

Divide each number until the remainder is one

Multiply the numbers used to divide which is 2 6 and 5 to get the LCM which is 60

Edit:

60 eggs /12 =5

60 muffins/10 =5

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

From the question, we have the following parameters that can be used in our computation:

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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Answer:

50

Step-by-step explanation:

Let's call the grizzly bear's normal heart rate x.

According to the problem, when the grizzly bear hibernates, its heart rate drops 10 beats per minute, which is 20% of its normal value. In other words, the amount that the heart rate drops is 20% of the normal heart rate.

We can set up an equation to represent this:

20% of x = 10

To solve for x, we can start by simplifying the left side of the equation. We can convert the percentage to a decimal by dividing by 100:

0.2x = 10

Then, we can isolate x by dividing both sides by 0.2:

x = 50

Therefore, the grizzly bear's normal heart rate when it is not hibernating is 50 beats per minute.

Answer:

50 bpm

Step-by-step explanation:

20% of a value is also 1/5 of a value.

Since the 10 bpm is 1/5 the normal value of the bear's heart rate, we just need to multiply 10 by 5 to get the normal heart rate:

10*5 = 50

Meaning that the bear's normal heart rate is 50 bpm.

The diagonal length should he use to make a door that fits in the door frame is √90 feet, Option 'B' is the correct answer.

What information do we have?

Length of door = 9 feet

Width of door = 3 feet

Using Pythagorean theorem,

H = √B² + P²

H = √3² + 9²

H = √9 + 81

H = √90 feet

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Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5

Answer:

Limit does not exist.

Step-by-step explanation:

From the graph, notice that the limit does not exist, when you move to the right the limit tend to -3 and when you approach from the left your limit approaches 4, therefore since the right and left limit are not equal the limit does not exist.

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

The profit made id each sign is sold for $20 is $4460

The profit model, P(x) = -10x² + 498x - 1,500

Where, x = price per sign sold

If the price per sign sold is $20. Hence, x = $20

The profit made can be calculated thus :

Put x = 20 in the profit function :

P(20) = -10(20)² + 498(20) - 1,500

P(20) = - 10(400) + 9960 - 1500

P(20) = - 4000 + 9960 - 1500

P(20) = $4,460

The profit made is $4,460

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Answer:

$4,460

Step-by-step explanation:

I got a 100% on my test

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Answer:

  4

Step-by-step explanation:

Put 2 where x is and do the arithmetic.

  f(2) = 10 -3∙2 = 10 -6

  f(2) = 4