what is the solution for the following equation 5x+7x=60

Answer:

64

Step-by-step explanation:

given 2 similar figures with ratio of heights a : b , then

ratio of volumes = a³ : b³

here ratio of heights is 1 : 4

ratio of volumes = 1³ : 4³ = 1 : 64

that is the volume of B is 64 times larger than the volume of A

There are a total of 45,144,000 (3 x 26 x 26 x 10 x 10) different character possibilities given the provided criteria.

To calculate the number of character possibilities, we'll break down each criterion and multiply the number of options for each position.

For the first position, we have 3 possibilities: the digits 1, 2, or 3.

For the second and third positions, we have 26 possibilities each, representing the 26 letters of the alphabet.

For the fourth and fifth positions, we have 10 possibilities each, representing the digits 0 through 9.

To find the total number of possibilities, we multiply the number of options for each position:

3 x 26 x 26 x 10 x 10 = 45,144,000.

Therefore, there are a total of 45,144,000 different character possibilities when considering the given criteria of having the options of 1, 2, or 3 for the first position, the 26 letters of the alphabet for the second and third positions, and the digits 0 through 9 for the fourth and fifth positions.

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A point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

option D is the correct answer.

The bottom right quadrant is the fourth quadrant, denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

So for coordinate plane in which Quadrant 1 is the top right quadrant, quadrant 2 is the top left, quadrant 3 is the bottom left, and quadrant 4 is the bottom right, a point with a positive x-coordinate and a negative y-coordinate will lie in Quadrant IV.

Thus, Quadrant IV is the correct answer because the x-axis has positive numbers and the y-axis has negative numbers.

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The value of the integral is [tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

The average rate of change over the interval [4, 10] is 3/2

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

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The integral expression is given as

[tex]\int\limits^{10}_4 {f(x)} \, dx[/tex]

So, we have

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[5 - 4]} \, dx[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[1]} \, dx[/tex]

Integrate

[tex]\int\limits^{10}_4 {f(x)} \, dx = [x]\limits^{10}_4[/tex]

Expand

[tex]\int\limits^{10}_4 {f(x)} \, dx = 10 - 4[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

Here, we have

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The interval is [4, 10]

So, we have

Average rate = (5 + 4)/(10 - 4)

Evaluate

Average rate = 3/2

Hence, the average rate of change is 3/2

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From the data given, the calculated mean of the distribution is 24.08 and the standard deviation of the binomial distribution is 3.7

Let's calculate the mean and standard deviation of a binomial distribution from the given data, we can use the formula;

Mean (μ) = n * P

Standard Deviation (σ) = √(n * P * (1 - P))

Given:

n = 56 (number of trials)

P = 0.43 (probability of success)

Calculating the mean:

Mean (μ) = n * P

Mean (μ) = 56 * 0.43

Mean (μ) = 24.08

The mean of the binomial distribution is 24.08.

Calculating the standard deviation:

Standard Deviation (σ) = √(n * P * (1 - P))

Standard Deviation (σ) = √(56 * 0.43 * (1 - 0.43))

Standard Deviation (σ) = √(24.08 * 0.57)

Standard Deviation (σ) = 3.7

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Answer:

96

Step-by-step explanation:

There are 2021 numbers and subtracting 7 each time, we will be left with 2021/7 ≈ 289 numbers

2021/3 = remainder 2

⇒2021 = 3x + 2

2021 - 7 = 3x + 2 - 7

= 3x - 5

= 3x - 3 - 2

= 3(x - 1) - 2

adding and sub 3,

= 3(x - 1) - 2 + 3 - 3

= 3(x - 1 - 1) + 1

=3(x - 2) + 1

The remainder is 1 and hence not divisible by 3

2021 - 7 - 7 = 3(x - 1) - 2 - 7

= 3(x - 1) - 9

= 3(x - 1 - 3)

= 3 (x - 4)

Remainderis 0 and hence divisible by 3

So, every 3rd number in the 289 numbers is divisible by 3

⇒ 289/3 ≈ 96

Cog counted 96 numbers

Answer: D. Rhombus

Step-by-step explanation: Based on the given image, the quadrilateral can be classified as a rhombus. A rhombus is a quadrilateral with all sides of equal length. In the given image, all four sides of the quadrilateral appear to be congruent, which satisfies the definition of a rhombus.

The value of K is 4.

In a regular polygon, all interior angles are congruent, which means they have the same measure. Let's denote the measure of each interior angle as A.

The sum of the interior angles of a polygon with (2x + 1) sides can be found using the formula:

Sum of interior angles = (2x + 1 - 2) * 180°

Since the polygon is regular, each interior angle has the same measure A. Therefore, we have the equation:

(2x + 1 - 2) * 180° = (2x + 1) * A

Simplifying the equation:

(2x - 1) * 180° = (2x + 1) * A

Now, we are given that the size of each interior angle is 140°. Substituting this value into the equation:

(2x - 1) * 180° = (2x + 1) * 140°

Solving for x:

360x - 180° = 280x + 140°

80x = 320°

x = 4

Therefore, the value of K is 4.

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Answer:

-5

Step-by-step explanation:

Simplify f(x)

[tex]f(x)=x^5-5x^4-17x^3+85x^2+16x-80\\f(x)=x^4(x-5)-17x^2(x-5)+16(x-5)\\f(x)=(x^4-17x^2+16)(x-5)\\f(x)=(x^2-16)(x^2-1)(x-5)\\f(x)=(x-4)(x+4)(x+1)(x-1)(x-5)[/tex]

Therefore, [tex]x=4,-4,-1,1,5[/tex] are the roots of the polynomial [tex]f(x)[/tex], which makes option 3 the best choice.

The number of possible license plates that can be issued using this system is 17,576,000.

To find the number of possible license plates that can be issued using this system, we need to determine the number of options for each character in the license plate.

For the first character, there are 26 letters in the English alphabet, so we have 26 options.

Similarly, for the second and third characters, we also have 26 options each.

For the fourth character, there are 10 possible numbers (0-9).

And for the fifth character, there are again 10 possible numbers.

To find the total number of possible license plates, we need to multiply the number of options for each character together.

Number of possible license plates = Number of options for the first character * Number of options for the second character * Number of options for the third character * Number of options for the fourth character * Number of options for the fifth character

Number of possible license plates = 26 * 26 * 26 * 10 * 10

Calculating this expression gives us:

Number of possible license plates = 17,576,000

Therefore, the number of possible license plates that can be issued using this system is 17,576,000.

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The correct statements that evaluate the report of the survey results are:A) The sample is biased because it does not represent the population. E) The question is biased towards a response of preferring to drink water after a game. Option A and E

Statement A) The sample is biased because it does not represent the population:

While the survey may have randomly selected 50 city soccer players from the soccer teams' rosters, it is important to consider whether these players truly represent the entire population of soccer players in the city.

Factors such as age, skill level, gender, and other demographic characteristics can affect the preferences of soccer players. If the sample is not diverse enough or does not adequately represent the population's composition, it may introduce bias and limit the generalizability of the survey results.

Statement E) The question is biased towards a response of preferring to drink water after a game:

The question itself introduces bias by explicitly mentioning water and a sports drink as the only options for post-game hydration. This could influence participants' responses by priming them to consider water as the default or more favorable choice.

The question should ideally be phrased in a neutral manner, allowing participants to provide their preferred choice without any suggestion or preference imposed by the question itself.

It is important to note that statements C) The sample is not biased, and D) The question is not biased, are incorrect. The sample can be considered biased due to potential limitations in its representativeness, and the question itself introduces bias by favoring one option over the other.

Option A and E

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Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

The measure of each angle indicated in the given triangle above would be given below as:

1.) ∅ = 21°

For question 1.

Using the Pythagorean formula such as:

C² = a²+b²

13² = a²+12²

a² = 169-144

= 25

a = √25 = 5

Using sine rule formula:

a/sinA = c/sinC

where;

a = 5

A = ?

c = 13

C = 90°

5/sin A = 14/sin 90

SinA = 5×1/14

SinA = 0.3571

A = Sin-1 (0.357142857)

= 21°

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Answer:

Average rate of change = 4/3

Step-by-step explanation:

The formula for the average rate of change (AROC) is given by:

AROC = f(b) - f(a) / b - a

Thus, we have f(5) - f(2) / 5 - 2

The y-coordinate when x = 5 is 7 so this is our f(5) value.

The y-coordinate when x = 2 is 3 so this is our f(2) value.

Now we can find the AROC:

AROC = (7 - 3) / (5 - 2)

AROC = 4 / 3

Thus, the average rate of change from x = 2 to x = 5 is 4/3.

Answer:

[tex]\huge\boxed{\sf 60}[/tex]

Step-by-step explanation:

10 • √64 – 5 • 4

We know that, √64 = 8

So,

= 10 × 8 - 5 × 4

In an expression, we follow the order of DMAS:

D => Division

M => Multiplication

A => Addition

S => Subtraction

So, here we will multiply first.

= 80 - 20

[tex]\rule[225]{225}{2}[/tex]

The values of x from the graph for which y = 0 are -3 and 4

From the question give above, we obtained the following:

The value of x from the graph can be obtained as follow:

y = x² - x - 12

but

y = 0

Thus, we have

x² - x - 12 = 0 (a quadratic function)

Thus, the vales of x will be the solutions of the equation x² - x - 12 = 0.

From the graph, the values of x when y = 0 will be the point when the line cuts across the x-axis.

From the graph, the line cuts across the x-axis at -3 and 4.

Thus, we can conclude that the value of x from the graph is -3 and 4.

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The ratios expressed in their simplest form are as follows:

Simplifying ratios involves reducing the given numbers to their lowest possible terms. Let's break down the calculations for each ratio:

1. Simplifying 15:35:

To find the greatest common divisor (GCD) of 15 and 35, we look for the largest number that evenly divides both 15 and 35.

The factors of 15 are: 1, 3, 5, 15.

The factors of 35 are: 1, 5, 7, 35.

The largest common factor between 15 and 35 is 5.

Divide both numbers by the GCD:

15 ÷ 5 = 3

35 ÷ 5 = 7

The simplified ratio is 3:7.

2. Simplifying 49:35:

Finding the GCD of 49 and 35:

The factors of 49 are: 1, 7, 49.

The factors of 35 are: 1, 5, 7, 35.

The largest common factor between 49 and 35 is 7.

Divide both numbers by the GCD:

49 ÷ 7 = 7

35 ÷ 7 = 5

The simplified ratio is 7:5.

3. Simplifying 1.3:45:

Since 1.3 is a decimal, it cannot be simplified further. The ratio remains as 1.3:45.

4. Simplifying 5mm:10cm:

Since 1cm is equivalent to 10mm, we can convert 10cm to 100mm.

Divide both the numerator and denominator by 5:

5mm ÷ 5 = 1mm

100mm ÷ 5 = 20mm

The simplified ratio is 1:20.

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Answer:33, 44, 55, 66

Step-by-step explanation:

Add 11 to the number in front. Its basically 11 x table, so:

11, 22, 33, 44, 55, 66, 77, 88, 99  

Answer:

11, 22, 33, 44, 55, 66, 77, 88, 99

Step-by-step explanation:

The pattern is x+11, so you just add 11 to the previous number.

The least score that Leon can achieve on his sixth exam and still earn an "A" is 93. He must score 93 or higher on his sixth exam to meet the requirement of accumulating at least 564 points in total.

To find the least score that Leon can achieve on his sixth exam and still earn an "A" in his Spanish course, we can set up an inequality.

Let x represent the score Leon receives on his sixth exam.

The total points Leon needs to accumulate to earn an "A" is 564.

Given his scores on the first five exams: 89, 96, 98, 95, and 93, we can add them up to find the total points earned so far:

89 + 96 + 98 + 95 + 93 = 471

To earn an "A," Leon needs a total of at least 564 points. Therefore, we can write the inequality:

471 + x ≥ 564

To solve for x, we'll isolate it on one side of the inequality:

x ≥ 564 - 471

x ≥ 93

Therefore, the least score that Leon can achieve on his sixth exam and still earn an "A" is 93. He must score 93 or higher on his sixth exam to meet the requirement of accumulating at least 564 points in total.

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Answer:

16 months

Step-by-step explanation:

In order to find the number of months it will take for Alma's bank account to reach $145, we can plug in 145 for y and solve for x:

Step 1:  Subtract 577 from both sides:

(145 = -27x + 577) - 577

-432 = -27x

Step 2:  Divide both sides by -27 to solve for x:

(-432 = -27x) / -27

16 = x

Thus, it will take 16 months for Alma's account to reach $145.

Answer:

is this right i mean im not very good at it but i hope this helped!

Step-by-step explanation:

:)

Answer:

∠ T = 46°

Step-by-step explanation:

the secant- secant angle T is half the difference of the measures of the intercepted arcs , that is

∠ T = [tex]\frac{1}{2}[/tex] (DR - ML) = [tex]\frac{1}{2}[/tex] (136 - 44)° = [tex]\frac{1}{2}[/tex] × 92° = 46°

I think 5x but I'm not sure

Answer:

Step-by-step explanation:

The answer is **-4**.

The number line shows that 2 is to the right of 6 on the number line. This means that 2 is greater than 6. To find the difference between 2 and 6, we can subtract 6 from 2. 2 - 6 = **-4**.

The other choices are incorrect. A is incorrect because 2 is greater than 6, so the difference between them cannot be 8. B is incorrect because 4 is the sum of 2 and 6, not the difference. C is incorrect because -3/4 is not a real number.

The measure of the interior angle c is equal to 30° considering the exterior angle 156.5° of the triangle.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

To calculate for the interior angle C°, we shall add C to the other interior angle which is also opposite the exterior angle 156.5 as follows:

C + 117.5 = 156.5

collect like terms

C = 156.5 - 117.5

C = 30°

In conclusion, the measure of the interior angle c is equal to 30° considering the exterior angle 156.5° of the triangle.

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The amount of money in the account after 9years to the nearest cent is $4826.69

Compound interest is the interest you earn on interest.

For example,if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

V = Pe^{rt}

V = 3980 e^{0.021 ×9}

V = 3989 e^{0.189}

V = 3989 × 1.21

V = $4826.69

Therefore the amount of money in the account after 9 years is $4826.69

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Answer: 18 meters

Let L be the length, w the width (all in meters).

Then you have L = 2w - 4, and 2l+2w =100. or L + w = 50. But L from the first relation into the second and simplify: 3w = 54 or w = 18.

Therefore, the width is 18 meters.

Happy to help; have a great day! :)

As per the given statement -

Let's assume that-

Formula used,

Substituting the values,

[tex] \longrightarrow[/tex] 2 (x + 2x - 4 ) = 100

[tex] \longrightarrow[/tex] 2(3x - 4) = 100

[tex] \longrightarrow[/tex] 3x - 4 = 100/2

[tex] \longrightarrow[/tex] 3x - 4 = 50

[tex] \longrightarrow[/tex] 3x = 50 + 4

[tex] \longrightarrow[/tex] 3x = 54

[tex] \longrightarrow[/tex] 3x = 54/3

[tex] \longrightarrow[/tex] x = 18

Since we have assumed width of the rectangle as 'x'.

So, The width of the rectangle is 18 m

The notation "<" represents a binary relation known as the "less than" relation.

It is a fundamental concept in mathematics and is used to compare the relative magnitudes or order of two elements.

In the context of numbers, the "<" symbol indicates that one number is strictly smaller or less than another. For example, in the expression "5 < 8," it means that the number 5 is less than the number 8.

The "<" symbol can also be used to denote other types of binary relations, depending on the context.

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The second coordinate of the given first coordinate is determined as;

f(0) = 1 and (1) = 0.7.

The second coordinate of the given first coordinate is calculated by applying the following method as follows;

The given function;

F(x) = 0.7ˣ

The value of f(0) is calculated as;

f (0) = 0.7⁰  = 1

The value of f(1) is calculated as;.

f (1) = 0.7¹ = 0.7

Thus, the second coordinate of the given first coordinate is determined by applying the appropriate substitute of the function as shown above.

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Answer:

[tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]

Step-by-step explanation:

Let [tex]\sin(2\arccos(-\frac{3}{5}))=\sin(2\theta)=2\sin\theta\cos\theta[/tex] and [tex]\theta=\arccos(-\frac{3}{5})[/tex] so that [tex]\cos\theta=-\frac{3}{5}[/tex]. Now we'll need to find [tex]\sin\theta[/tex] having known [tex]\cos\theta[/tex]:

[tex]\displaystyle \cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{-3}{5}\\\\\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{\sqrt{5^2-(-3)^2}}{5}=\frac{\sqrt{25-9}}{5}=\frac{\sqrt{16}}{5}=\frac{4}{5}[/tex]

Therefore, [tex]2\sin\theta\cos\theta=2(\frac{4}{5})(-\frac{3}{5})=2(\frac{-12}{25})=-\frac{24}{25}[/tex], which makes [tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]