verbal expression for the following numerical expression: ( 4 + 9 ) x 3

Answer:

16. A and C; 17. All triangles

Step-by-step explanation:

Reflection over x is just "flipping upside-down as if turning the page over holding the ends of x axis", so it's A and C

Congruent means "have same sides and angles" and all the triangles are the same that way.

The probability that 3 of 8 stolen cars will be recovered is 0.296 or approximately 0.30.

The given problem involves a binomial distribution, where the probability of success (recovering a stolen car) is p = 0.78 and the number of trials is n = 8. We need to find the probability of getting exactly 3 successes.

The probability of getting exactly k successes in n trials can be calculated using the binomial probability formula:

P(k successes) = (n choose k) * \(p^k\) * \({1-p}^{n-k}\)

where (n choose k) represents the binomial coefficient, which can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

where n! represents the factorial of n.

Using the above formula with k = 3, n = 8, and p = 0.78, we get:

P(3 successes) = (8 choose 3) * 0.78³ * (1-0.78)⁵

= 56 * 0.78³ * 0.22⁵

= 0.296

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Answer:

The sum is $10

Step-by-step explanation:

Since Tony got $5 on Monday and $5 on Tuesday, we can add them together by doing 5+5. We can add 5 and 5 together to get a total of $10 that Tony has earned. This means that it isn't a sum of 0 but a sum of 10.

(hope this helped)

Answer:

168 in

Step-by-step explanation:

Pythagoras says:

b² + 56² = 70²

so

b² = 70² - 56²

b = √1764 = 42

so the perimeter is 70+56+42 = 168

Answer:

EKH and FKG

Step-by-step explanation:

vertical angles are angles that are directly vertical from each other.

Answer:

C

Step-by-step explanation:

EKH AND FKG THEY ARE VERTICLE (SAME ANGLES)

Triangles can be inscribed in and circumscribed around circles, and circles can be inscribed in and circumscribed around triangles.

There are several relationships between triangles and circles, including:

Incenter: The incenter of a triangle is the center of the circle that is tangent to all three sides of the triangle.

Circumcenter: The circumcenter of a triangle is the center of the circle that passes through all three vertices of the triangle.

Orthocenter: The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The circumcircle of a triangle passes through the orthocenter.

Inscribed angle: An inscribed angle of a circle is an angle whose vertex lies on the circle, and whose sides are chords of the circle. The measure of an inscribed angle is half the measure of the intercepted arc.

Tangent: A tangent to a circle is a line that intersects the circle at exactly one point. If a line is tangent to a circle at a point, then it is perpendicular to the radius at that point.

Similarity: If two triangles are inscribed in the same circle and share a common chord as a side, then they are similar.

These relationships have important applications in geometry and trigonometry, and can be used to solve problems involving triangles and circles.

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Answer:

Perimeter = 4.5√3 + 4.5

Area = 3.375√3

Step-by-step explanation:

Well you can first see that triangle ABC is a 30°60°90° triangle.

Since angle A is 60 and it is bisected, you will have a small 30°60°90° triangle and a 120°30°30° triangle.

You can say that DA is congruent to BD by Base Angle Theorem.

DA = 3

By using the ratios of the sides of the 30°60°90° you get that CD is 1.5 and CA is 1.5√3

CD = 1.5

CA = 1.5√3

BC = 4.5

Area = (4.5 * 1.5√3) / 3 = 6.75√3 / 2

Area = 3.375√3

By using the 30°60°90° ratio again, you get that BA = 3√3

Perimeter = 1.5√3 + 3√3 + 4.5

Perimeter = 4.5√3 + 4.5

I'm not 100% sure that the answer is right so check it.

Answer:

x=-3 or 4

Step-by-step explanation:

A) The general solution of the differential equation is y = 4 + C * \(sqrt(e^(-t/2)),\) where C is an arbitrary constant.

B) The particular solution with the initial condition y(0) = 5 is y = 4 + \(sqrt(e^(-t/2)).\)

C) The equilibrium y(t) = 0 is not reached, and the system exhibits stability as y(t) tends to converge to 4 as t increases.

A) To find the general solution of the differential equation, we can use the method of integrating factors. The given equation is a first-order linear ordinary differential equation of the form:

dy/dt + (1/2)y = 2

First, we identify the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient is (1/2). So, the integrating factor (IF) is given by:

\(IF = e^(integral(1/2) dt) = e^(1/2 * t) = sqrt(e^(t/2))\)

Now, we multiply both sides of the differential equation by the integrating factor:

\(sqrt(e^(t/2)) * (dy/dt) + (1/2)sqrt(e^(t/2)) * y = 2 * sqrt(e^(t/2))\)

By applying the product rule on the left-hand side, we can rewrite the equation as:

\((d/dt)(sqrt(e^(t/2)) * y) = 2 * sqrt(e^(t/2))\)

Integrating both sides with respect to t:

\(sqrt(e^(t/2)) * y = 4 * sqrt(e^(t/2)) + C\)

Where C is the constant of integration. Now, we solve for y:

\(y = (4 * sqrt(e^(t/2)) + C) / sqrt(e^(t/2))\)

Simplifying further:

y = 4 + C * \(sqrt(e^(-t/2))\)

Therefore, the general solution of the differential equation is y = 4 + C *sqrt(e^(-t/2)), where C is an arbitrary constant.

B) To find a particular solution with the initial condition y(0) = 5, we substitute t = 0 and y = 5 into the general solution:

5 = 4 + C * \(sqrt(e^0)\)

5 = 4 + C * sqrt(1)

5 = 4 + C

From this, we find C = 1.

Thus, the particular solution with the initial condition y(0) = 5 is y = 4 + sqrt(e^(-t/2)).

C) To determine the value of y(t) at the equilibrium y(t) = 0, we set y = 0 in the general solution:

\(0 = 4 + C * sqrt(e^(-t/2))\)

Solving for t, we have:

\(C * sqrt(e^(-t/2)) = -4\)

Since C is a constant and the square root of a positive quantity is always positive, there is no value of t for which y(t) will be exactly equal to 0. Therefore, the equilibrium y(t) = 0 is not reached.

Regarding stability, we can observe that the exponential term \(e^(-t/2)\)in the general solution decays to 0 as t approaches infinity. This indicates that y(t) will tend to converge to 4 as t increases, suggesting stability. However, it's important to note that the equilibrium at y(t) = 0 is not reachable in this case.

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It seems that you are referring to the exponential growth formula which is:

N(t) = N₀ * (1 + r)^t

Where:
N(t) is the number of individuals at time t
N₀ is the initial number of individuals (in this case, 25 alive in 1955)
r is the growth rate
t is the time period (in years)

In this problem, we have:
N₀ = 25 individuals (alive in 1955)
N(t) = 500 individuals (existed in 2013)
t = 2013 - 1955 = 58 years

We need to solve for r. To do that, rearrange the formula:

r = [(N(t) / N₀)^(1/t)] - 1

Plug in the given values:

r = [(500 / 25)^(1/58)] - 1

r ≈ 0.029

So, the answer is (d) 0.029.

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After one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

To calculate the amount of money you will have in the savings account after one year with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Let's solve it step by step:

Given:

P = $3,000 (principal amount)

r = 6% = 0.06 (annual interest rate as a decimal)

n = 1 (compounded annually)

t = 1 (one year)

Using the formula:

A = 3000 * (1 + 0.06/1)^(1*1)

A = 3000 * (1 + 0.06)^1

A = 3000 * (1.06)^1

A ≈ $3180

So, after one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

It seems there was a discrepancy in the answer provided. Based on the given information, the correct calculation yields $3,180, not $5,372.54.

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Answer:

51

Step-by-step explanation:

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

\( \frac{8}{25} \)

Explanation

\( \frac{0.32}{100} \)

2 numbers are beyond the decimal point. This is in the hundredths place. So place the decimal upon 100. It will become

\( \frac{32}{100} \)

To simplify this fraction find the lowest common multiple that can go both in 32 and a 100 without leaving a remainder. That would be 4.

32 ÷ 4 = 8

100÷4 = 25

Answer:

x=-5

Step-by-step explanation:Step 1: Simplify both sides of the equation.

8x−5(4x+3)−(3−2x)=4−4(2x−3)−(9−3x)

8x−5(4x+3)+−1(3−2x)=4−4(2x−3)+−1(9−3x)(Distribute the Negative Sign)

8x+−5(4x+3)+(−1)(3)+−1(−2x)=4+−4(2x−3)+(−1)(9)+−1(−3x)

8x+−5(4x+3)+−3+2x=4+−4(2x−3)+−9+3x

8x+(−5)(4x)+(−5)(3)+−3+2x=4+(−4)(2x)+(−4)(−3)+−9+3x(Distribute)

8x+−20x+−15+−3+2x=4+−8x+12+−9+3x

(8x+−20x+2x)+(−15+−3)=(−8x+3x)+(4+12+−9)(Combine Like Terms)

−10x+−18=−5x+7

−10x−18=−5x+7

Step 2: Add 5x to both sides.

−10x−18+5x=−5x+7+5x

−5x−18=7

Step 3: Add 18 to both sides.

−5x−18+18=7+18

−5x=25

Step 4: Divide both sides by -5.

−5x −5 = 25 −5

x=−5

Answer: I believe the answer is 30

Step-by-step explanation:

you set them equal to each other

3x +5=4x -35

3x=4x-30

-x = -30

x= 30

Answer:

a + \(11^{3}\)

or

a + 1331

Step-by-step explanation:

The sum of 11 cubed and a

\(11^{3}\) + a

or

1331 + a

Answer:

120

Step-by-step explanation:

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

Answer:

\(y = - \frac{ {x}^{2} }{16} \)

Step-by-step explanation:

First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards

Equation of a Parabola with center (h,k) >

\((x - h) {}^{2} = - 4p(y - k)\)

Where p is the distance of the vertex to focus/ or distance to vertex to directrix

This emans that the vertex is halfway of (-4,0) and x=4.

Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that

The vertex is halfway between (-4,0) and (4,0).

So the vertex is (0,0).

Plugging that in we get,

\( {x}^{2} = - 4py\)

The distance to the vertex or either the focus or directrix is 4 so p=4

\( {x}^{2} = - 4(4)y\)

\( {x}^{2} = - 16y\)

\(y = - \frac{ {x}^{2} }{16} \)

Answer:

x = -3

Step-by-step explanation:

To answer this question, you should first remember that the inside angles of a triangle will always add up to 180 degrees. Therefore, we can make an equation and solve it form there:

55 + 54 + (x + 74) = 180

We add like terms:

109 + (x + 74) = 180

Continue adding like terms:

183 + x = 180

Next, we dubtract to siolate the "x" variable:

x = -3

Hope this helps :)

x=-3

Step-by-step explanation:

To start off, you're going to want to know and understand that all the angles of triangle equal 180 degrees.

Now that we know a triangle equals 180 degrees, lets make an equation. This is equation can be 55+54+74+x=180.

Now, lets combine the like terms in the equation. The equation now becomes 183+x=180.

From here, we subtract 180 from both sides, which would get us x=-3.

To double check that this is correct and that it works, you can plug in the -3 where the x would be.

I hope this helped!! Let me know if you have any further questions.

The weight of the melted ice cream would be the same as the weight of the original ice cream, which is 5 ounces.

a quantity or thing weighing a fixed and usually specified amount. : a heavy object (such as a metal ball) thrown, put, or lifted as an athletic exercise or contest. 3. : a unit of weight or mass see Metric System Table.

When the ice cream melts, it undergoes a change in state from solid to liquid, but the total mass or weight remains unchanged. Therefore, the weight of the melted ice cream is still 5 ounces.

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The solution to the system of equations is (-6, -9).

Given y=2x+3,

we are to find the solution to the system of equations.

In order to find the solution to the system of equations,

we require another equation in the system.

The system of equations is:

y = 2x + 3 ...

(1)Let's assume another equation:y - 3x = 9 ...

(2)The given system of equations is:

y = 2x + 3 ... (1)y - 3x = 9 ...

(2)Substituting equation (1) into equation (2), we get:

(2x + 3) - 3x = 9 => -x + 3 = 9 => -x = 9 - 3 => -x = 6 => x = -6

Therefore, substituting this value of x in equation (1), we get:

y = 2x + 3 => y = 2(-6) + 3 => y = -12 + 3 => y = -9

Therefore, the solution to the given system of equations is (-6, -9).

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Answer:

33 miles

Step-by-step explanation: I think it is correct

Monday: 3 miles

Tuesday: 10 miles

Wednesday: 20 miles because 10 x 2 = 20

3 miles + 10 miles + 20 miles = 33 miles

Hope this helps!

Answer:

intersection of the lines drawn to bisect each vertex of the triangle

Step-by-step explanation:

trust

The value of n in the geometric sequence is 10.

The first term of the sequence is 7, the common ratio is 2 and the nth term is 3584. Therefore, the value of n can be found as follows:

using geometric progression formula,

aₙ = arⁿ⁻¹

where

Therefore,

3584 = 7 × 2ⁿ⁻¹

divide both sides by 7

2ⁿ⁻¹ = 3584 / 7

2ⁿ⁻¹ = 512

2ⁿ⁻¹  = 2⁹

n - 1 = 9

n = 9 + 1

Therefore,

n = 10

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Step-by-step explanation:

∠2 = 77°

∠2 = ∠4 ( being vertically opposite angle )

∠4 = 77°

Now...

∠1 + ∠2 = 180° ( supplementary angle )

∠1 = 180° - 77°

∠1 = 103°

here....

∠1 = ∠3 ( vertically opposite angle )

∠1 = 103°

\(.....\)