ABC is an isosceles triangle: AC = 13cm. What is the length of AB?

To find the number of heart stickers in a pack of 140 stickers, we can use proportions. We can set up the proportion by using the number of stickers on the sheet of 28 stickers as the denominator and the number of heart stickers on the sheet of 28 stickers as the numerator. The proportion will look like this:

Copy code

(heart stickers in a pack of 140 stickers) / 140 = 16 / 28

To solve for the number of heart stickers in a pack of 140 stickers, we can first multiply both sides of the equation by 140 to get rid of the denominator on the left side:

(heart stickers in a pack of 140 stickers) = 140 * 16 / 28

Then, we can simplify the expression on the right side by dividing the numerator and denominator by 4 to get:

(heart stickers in a pack of 140 stickers) = 35

Therefore, a pack of 140 stickers would have 35 heart stickers.

If someone told you that the derivative (slope of the tangent line to the graph) of f(x) at x=1 was −1/n² for some integer n, we would expect n to be equal to 2.

We have:

f(x) = 1/(x-3)

Using the difference quotient formula, we get:

f(1+h) = 1/(1+h-3) = 1/(h-2)

f(1) = 1/(1-3) = -1/2

Therefore, the difference quotient formula becomes:

f(1+h) - f(1) / h = [1/(h-2) + 1/2] / h - 1/2h = (3 - h) / 2h(h - 2)

Plugging in h = 0.1, we get:

f(1.1) - f(1) / 0.1 = 2.6525

Plugging in h = 0.01, we get:

f(1.01) - f(1) / 0.01 = 2.525

Plugging in h = -0.01, we get:

f(0.99) - f(1) / (-0.01) = -2.525

Plugging in h = -0.1, we get:

f(0.9) - f(1) / (-0.1) = -2.6525

The derivative of f(x) at x=1 is:

f'(x) = -1/(x-3)^2

Plugging in x=1, we get:

f'(1) = -1/(-2)^2 = -1/4

Therefore, we would expect n to be equal to 2.

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the right answer is c

Answer:

The slope is 2.

Step-by-step explanation:

You can see on the intercepts that it goes rise 2 and run over 1 which would basically equal to 2.

Step-by-step explanation:

I don't know if it help but here.It's the one that says slope of a line.

Answer:

D or 3800

Step-by-step explanation:

Just divided 855 by 45 then multiplied 200 by 19

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Answer:

1/6

Step-by-step explanation:

We know that a die has 6 sides. What would be the probability to roll 1 of those sides? (to rephrase the question)

well. the probability to roll one of the sides on a 6 side dice is 1/6, 1 side on the 6 sided die.

Answer:

1/6

Step-by-step explanation:

There are six possible outcomes when rolling a die

1,2,3,4,5,6

P(rolling a 2) = number of outcomes that is a 2/ total outcomes

                     = 1/6

By using unitary method, it can be calculated that

heart beats 1 time in 0.359 seconds

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

In 1 minute number of beats in heart  is 167 beats

In 60 seconds number of beats in heart is 167 beats

A heart beats 167 times in 60 seconds

A heart beats 1 time in 60/167 seconds

A heart beats 1 time in 0.359 seconds

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Answer:

y = 5, 3

x = 155, 171

(y = 5, x = 155)

(y = 3, x = 171)

Step-by-step explanation:

(8y - 15) = (y²)

-8y + 15          -8y + 15

--------------------------------

y² - 8y + 15 = 0

(y - 5) (y - 3) = 0

--------------

y = 5, 3

----------------------------------------------------------------------------------------------------------

y² + x = 180

(5)² + x = 180

25 + x = 180

-25         -25

--------------------

x = 155

(3)² + x = 180

9 + x = 180

-9            -9

------------------

x = 171

----------------------------------------------------------------------------------------------------------

I really hope this helps!

Answer:

0.37 rad m

Step-by-step explanation:

Answer:

Step-by-step explanation:

Arc length formula:

We have:

Finding the length of arc AB:

the base is 6ft of the billboard

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

If a road map has a scale of 3 inches to 100 miles.

Then the scale factor is given as,

Sclar factor = 100 / 3

Sclar factor = 33.33 miles per inch

Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,

Distance = 33.33 x 4.5

Distance = 150 miles

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

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Step-by-step explanation:

\(y + (z - 7) {}^{2} \times 2 \\ 3 + (9 - 7) {}^{2} \times 2 \\ 3 + (2) {}^{2} \times 2 \\ 3 + 4 \times 2 \\ 3 + 8 = 11\)

Answer:

We have to:

"All of the plots are the same length, x"

L = x

"and the width of each plot is 5 yards less than the length"

W = x-5

"The total number of plots Liam owns is 20 more than the length of a plot"

20 + x

"the total area of all the plots Liam owns is 2,688 square yards"

A = (20 + x) * (x) * (x-5)

A = (20x - 100 + x ^ 2 -5x) * (x)

A = (x ^ 2 + 15x - 100) * (x)

2688 = (x ^ 3 + 15x ^ 2 - 100x)

x ^ 3 + 15x ^ 2 - 100x = 2688

x ^ 3 + 15x ^ 2 - 100x - 2688 = 0

Answer:

*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.

Answer:x^3+15x^2-100x-2,688=0

Step-by-step explanation:

The number of downloads of the high quality version that was made was 600.

This is a great system of equations problem

If we call the number of standard version downloads (S)  

The high quality downloads (H).

To find S, we can rearrange the first statement to H = 910 - S,

Then we would substitute (910 - S) wherever you see an H in the second equation so that you have only S's in your equation.

Thus:

2.8(S) + 4.4(910 - S) = 3044

2.8S + 4004 - 4.4S = 3044

-1.6S = -960

s = 600

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The arithmetic mean provides a single measure for a certain population, also called the average.

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The ratio of the total number of observations divided by the sum of all the given observations is known as the arithmetic mean. For instance, if the data set contains 5 observations, it is possible to get the arithmetic mean by adding all 5 of the given observations and dividing by 5.

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As a linear combination of the orthonormal basis vectors discovered in part (a), write v = (3, 1, 2) in this format. Therefore,

(a) Using the Gram-Schmidt process, the orthonormal basis for ℝ³ is \(\left{ \left( -1, 0.1 \right) \div \sqrt{1.01}, \left( 0.282, -0.028 \right) \div \sqrt{5.3664} \right}\)}.

(b) The vector v = (3, 1.2) can be approximated as \(v \approx -2.9175 \cdot \frac{(-1, 0.1)}{\sqrt{1.01}} + 0.2698 \cdot \frac{(0.282, -0.028)}{\sqrt{5.3664}}\).

(a) To find an orthonormal basis for ℝ³ using the Gram-Schmidt process, we start with the given basis vectors and follow these steps:

Step 1: Normalize the first vector

Let's normalize the first vector (-1, 0.1):

\(v_1 = \frac{(-1, 0.1)}{\left\| (-1, 0.1) \right\|}\)

The magnitude of \(\[(-1, 0.1) = \|(-1, 0.1)\| = \sqrt{(-1)^2 + (0.1)^2} = \sqrt{1 + 0.01} = \sqrt{1.01}\]\)

So, \(v_1 = \frac{(-1, 0.1)}{\sqrt{1.01}}\)

Step 2: Project and subtract from the second vector

Now, we project the second vector (1, 2, -1) onto v₁ and subtract that projection from the second vector:

\(\text{proj}_{v_1} v_2 &= \left((1, 2, -1) \cdot v_1\right) v_1 \\\\v_2' &= (1, 2, -1) - \text{proj}_{v_1} v_2\)

The dot product of (1, 2, -1) and v₁ is ((1)(-1) + (2)(0.1) + (-1)(0)) = -1 + 0.2 + 0 = -0.8

\(\text{proj}_{v_1}^{v_2} &= (-0.8) v_1 \\&= (-0.8)(-1, 0.1) / \sqrt{1.01} \\&= \left( \frac{0.8}{\sqrt{1.01}}, -\frac{0.08}{\sqrt{1.01}} \right)\)

\(v_2' = (1, 2, -1) - \frac{(0.8, -0.08)}{\sqrt{1.01}}\)

Step 3: Normalize the resulting vector

Now, we normalize the resulting vector v₂' obtained in the previous step:

\(v_2 = \frac{v_2'}{\left\| v_2' \right\|}\)

The magnitude of \(\[v_2' = \|v_2'\| = \sqrt{0.2^2 + 2.08^2 + (-1)^2} = \sqrt{0.04 + 4.3264 + 1} = \sqrt{5.3664}\]\)

So, \(\[v_2 = \frac{v_2'}{\sqrt{5.3664}}\]\)

Now we have an orthonormal basis {v₁, v₂}.

(b) To express v = (3, 1.2) as a linear combination of the orthonormal basis vectors {v₁, v₂} obtained in part (a), we can use the following equation:

v = c₁ * v₁ + c₂ * v₂

Let's solve for c₂ and c₂:

v = c₁ * v₁ + c₂ * v₂

(3, 1.2) = c₁ * v₁ + c₂ * v₂

To find c₁ and c₂, we can take the dot product of both sides with v₁ and v₂:

(3, 1.2) · v1 = (c₁ * v₁ + c₂ * v₂) · v₁

(3, 1.2) · v₂ = (c₁ * v₁ + c₂ * v₂) · v₂

The dot products simplify to:

3 = c₁ * (v₁ · v₁)

1.2 = c₂ * (v₂· v₂)

Since v₁ and v₂ are orthonormal, their dot products with themselves are 1:3 = c₁

1.2 = c₂

Therefore, the linear combination is:

v = 3 * v₁ + 1.

2 * v₂

Substituting the values of v₁ and v₂:

\([3 \cdot \left( \frac{(-1, 0.1)}{\sqrt{1.01}} \right) + 1.2 \cdot \left( \frac{v_2'}{\sqrt{5.3664}} \right)]\)

Simplifying the expression, we have:

v ≈ \(\[(-2.97, 0.297) + \frac{(0.282, -0.028)}{\sqrt{5.3664}}\]\)

Adding the components together:

v ≈ \(\[\left( -2.97 + \frac{0.282}{\sqrt{5.3664}}, 0.297 - \frac{0.028}{\sqrt{5.3664}} \right)\]\)

So, v ≈ (-2.97 + 0.0525, 0.297 - 0.0272) ≈ (-2.9175, 0.2698)

Therefore, v ≈ (-2.9175, 0.2698) can be expressed as a linear combination of the orthonormal basis vectors found in part (a).

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Answer:

the last choice is the 6th term of expression

Step-by-step explanation:

all the work and steps is in the pic go check it out sorry if wrong and have a  wonderful day:)

The critical value for an F-test at α = 2.5% significance with one independent variable and 27 observations is approximately 5.7033. It represents the threshold beyond which we reject the null hypothesis in favor of the alternative hypothesis.

To determine the critical value for an F-test at α = 2.5% significance, we need to know the degrees of freedom associated with the numerator and denominator of the F-statistic.

For an F-test, the numerator degrees of freedom (df1) correspond to the number of groups or treatment conditions minus 1. In this case, since there is only one independent variable, the number of groups is 2 (assuming a standard F-test), so df1 = 2 - 1 = 1.

The denominator degrees of freedom (df2) correspond to the total number of observations minus the number of groups. In this case, we have n = 27 observations and 2 groups, so df2 = 27 - 2 = 25.

Now we can use these degrees of freedom values and the significance level (α) to find the critical value using an F-table or calculator.

Using statistical software or an online calculator, the critical value for an F-test with df1 = 1 and df2 = 25 at α = 2.5% significance is approximately 5.7033 (rounded to four decimal places).

Therefore, the critical value for the F-test at α = 2.5% significance is 5.7033.

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Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

The perimeter of the rectangle is 16.697 meters.

It is given that A rectangle is 30m and 70m. Hence, the area of the rectangle is length × breadth

= 30 × 70 = 2100 square meters.

The fact that a square's area equals a rectangle's area is a given.

Thus the area of the square = 2100. Hence it's side is root of 2100 which is 45.82575 meters.

To find how much the perimeter of the rectangle exceeds the perimeter of the square, we need to find out each perimeter first.

Rectangle perimeter = 2(l + b)

= 2(30 + 70)

= 200 meters.

Square perimeter = 4 * side

= 4 × 45.82575

= 183.303 meters.

Thus it's perimeter exceeds by 200 - 183.303 = 16.697 meters.

It exceeds by 16.697 meters.

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Answer:

The hand moved \(\bf \frac{3}{4}\) of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     \(\frac{1}{12}\) turns

9 hours     ⇒     \(\frac{1}{12}\)  × 9 = \(\frac{9}{12}\)

                                     = \(\bf \frac{3}{4}\) turns    (simplified)

∴ The hand moved \(\bf \frac{3}{4}\) of a complete turn.

The answer is  \(\boxed{\frac{3}{4}}\).

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

Answer:

26. 30 ≥ 7.5a + 4.5s         28. $22.50

Step-by-step explanation:

26. The family doesn't want to spend over 30 dollars, so when writing the inequality the amount they spend needs to be less than or equal to 30, hence the greater than/equal to sign. When writing the expression a - amount of adults & s - amount of students.

*remember in the question it states middle and high schoolers both count as students

The 7.5 is cost for adults and the 4.5 is cost for students.

28. You can use the expression created in 26

7.5a + 4.5s

Then substitute in the amount of people into their respective categories.

7.5(2) + 4.5(3) = 22.50

The width of the plainfield is 56 yards, and the length is 216 yards.

Let's start by defining the variables we'll need to solve the problem. We'll use "P" to represent the perimeter of the plainfield, "l" to represent the length of the field, and "w" to represent the width of the field.

From the problem statement, we know that the perimeter of the plainfield is 544 yards, so we can write:

P = 544

The perimeter of a rectangle is given by the formula P = 2(l + w), so we can substitute our variables and get:

2(l + w) = 544

Simplifying this expression, we get:

l + w = 272

Now we need to use the information given about the relationship between the length and width of the field to write an equation that relates the two variables. We know that the length is 8 yards less than a quadruple of the width, so we can write:

l = 4w - 8

We can substitute this expression for "l" in the equation we derived earlier:

l + w = 272

(4w - 8) + w = 272

5w - 8 = 272

5w = 280

w = 56

So the width of the field is 56 yards. We can use the equation we derived earlier to find the length:

l = 4w - 8

l = 4(56) - 8

l = 216

So the length of the field is 216 yards.

Therefore, the width of the plainfield is 56 yards, and the length is 216 yards.

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Answer: Choice A

========================================================

Explanation:

A perfect square trinomial is of the form

(m+n)^2 = m^2 + 2mn + n^2

We can see why this works through use of the FOIL rule.

So the first and last terms must be perfect squares, and they must be positive. This rules out choices B and D since we have -4 and -9 as those last terms being negative.

Choice C is ruled out because the middle coefficient -9 isn't correct. The middle coefficient must be some even number since 2 is a factor of 2mn.

This leaves choice A. We can do a bit of trial and error to find that

(x-2)^2 = x^2 - 4x + 4

showing that choice A is a perfect square trinomial.

Answer:

A) x² - 4x + 4

Step-by-step explanation:

Given the following special factoring formulas on perfect square trinomials:

u² + 2uv + v² = (u + v)²

u² - 2uv + v² = (u - v)²

Apply these concepts on the given set of equations to see which special factoring formulas apply on the given options. I will only work on one of the given options, and you could apply these same techniques on the other ones to compare the results with your calculations.

To find the binomial factors of quadratic equations, you must find factors with product uv, and sum v.

In Option A: x² - 4x + 4

Right off the bat, it seems like the difference of squares may apply to this equation.  You must find the factors that will product of 4 and a sum of -4.

The possible factors are:

product uv: -2 × -2  = 4,

sum v :  -2 + -2 = -4

Hence, the binomial factor of x² - 4x + 4 =  (x - 2)²

If you expand this binomial through FOIL method:

(x - 2)(x - 2) = x² - 2x - 2x + 4 = x² - 4x + 4

This means that the trinomial x² - 4x + 4 produces a perfect square binomial factors of (x - 2)².

Therefore, the correct answer is Option A) x² - 4x + 4.

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Answer: C

Step-by-step explanation:

1 lb = 16 oz

2 lb = 32 oz

18 oz = 18 oz

49 oz = 49 oz

I am not a professional, I am simply using prior knowledge!

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In a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

It should be noted that a hypothesis is simply used to get information about a certain thing.

In this case, in a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

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Answer:

(3x+1)(x+5)

Step-by-step explanation:

Sorry for my handwriting lol hope this makes sense

Robert, Juan, Susan, and Linda scored above the mean, Joel scored on the mean, and Jan scored below the mean on the advanced first aid course's final exam based on their z-score. Their final exam scores were 172, 184, 190, 150, 166, and 182, respectively.

The students with positive z-scores scored above the mean. So, Robert, Juan, Susan, and Linda scored above the mean. The student with a z-score of 0.00 scored on the mean. So, Joel scored on the mean. The student with a negative z-score scored below the mean. So, Jan scored below the mean.

To find the final exam score for each student, we can use the formula:

z = (x - m) / s

where z is the z-score, x is the final exam score, m is the mean score, and s is the standard deviation.

Rearranging the formula, we get:

x = z * s + m

Using the given values of z, s, and m, we can find the final exam score for each student:

Robert: x = 1.10 * 20 + 150 = 172

Juan: x = 1.70 * 20 + 150 = 184

Susan: x = 2.00 * 20 + 150 = 190

Joel: x = 0.00 * 20 + 150 = 150

Jan: x = 0.80 * 20 + 150 = 166

Linda: x = 1.60 * 20 + 150 = 182

So, the final exam scores for Robert, Juan, Susan, Joel, Jan, and Linda are 172, 184, 190, 150, 166, and 182, respectively.

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