Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range? a. No: we would have no information about the domain. c. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≤ n. b. No: we would need to know if the vertex is a minimum or a maximum. d. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≥ n.

The probability that the product of the numbers on the top faces of four standard six-sided dice will be prime is approximately 0.09%.

To calculate this probability, a table can be created that outlines the 36 possible combinations of numbers on the top faces of four dice. From this table, the number of prime products can be determined. As there are only three primes (2, 3, and 5) in the 36 possible products, the probability of rolling a prime product is 3/36, which is approximately 0.09%. This means that the probability of rolling a prime product on four standard six-sided dice is very low, approximately 0.09%.

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Answer: 42

Step-by-step explanation:

70% = 70/100 as a fraction. 60 is 60/1 as a fraction.

Using this information, set up your question.

--> 70/100 x 60  

Multiply the fractions together and you get 4200/100. This then simplifies/is equivalent to 42. Therefore, 70% of 60 is 42.

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

The main difference between bar charts and histograms lies in the type of data they represent. Bar charts are used for categorical data, where each bar represents a distinct category. On the other hand, histograms are used for continuous or numerical data, where the bars represent intervals or ranges of values.

Bar charts are graphical representations that use rectangular bars to compare different categories. Each bar represents a separate category, and the height of the bar indicates the frequency, count, or proportion associated with that category. Bar charts are commonly used to display categorical data, such as comparing sales figures for different products or survey responses across different options.

Histograms, on the other hand, are graphical representations that display the distribution of numerical data. Instead of representing distinct categories, histograms group the data into intervals or bins along the x-axis. The height of each bar in a histogram represents the frequency or count of data points falling within that particular interval. Histograms are useful for visualizing the shape, central tendency, and spread of continuous data, such as exam scores, temperatures, or ages.

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A reliable test is one that can measure what it is supposed to measure consistently, yield the same results when given a second time, and provide an unbiased score, ensuring that the results obtained are valid and reliable. Answer is D.

The reliability of a test refers to its consistency and stability over time and under different conditions. It is the extent to which a test is able to yield the same results repeatedly. A reliable test should be able to measure what it is supposed to measure consistently, without any errors or fluctuations. Additionally, it should provide an unbiased score, which means that it should not be influenced by any external factors such as personal biases or environmental factors. Therefore, the answer to the question is D, all of the above.

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Answer:

A.)

Rise = 2

Run = 5

m = 2/5

B.)

Rise = 2

Run = - 4

m = - 1/2

C.)

Rise = 3

Run = 1

m = 3

Step-by-step explanation:

Rise = y2 - y1

Run = x2 - x1

Slope, m = Rise / Run

A.) (0,0) ; (5 2)

x1 = 0 ; y1 = 0

x2 = 5 ; y2 = 2

Rise = 2 - 0 = 2

Run = 5 - 0 = 5

m = 2/5

B.) (1, 2) ; (-3, 4)

x1 = 1 ; y1 = 2

x2 = - 3 ; y2 = 4

Rise = 4 - 2 = 2

Run = - 3 - 1 = - 4

m = 2/-4 = - 1/2

C.) (5,2) ; (6,5)

x1 = 5 ; y1 = 2

x2 = 6 ; y2 = 5

Rise = 5 - 2 = 3

Run = 6 - 5 = 1

m = 3/1 = 3

The percentage that Sullivan family spends is 60% of their net monthly income on food, clothing, and housing.

What is the definition of percentage?

A percentage is expressed by a fraction of 100. It is represented by the symbol "%." The word "percent" comes from the Latin per centum, which means "by the hundred."

Now,

The total amount spent on food, clothing, and housing is:

Total = 936 + 1,248 + 2,496 = 4,680

To find the percentage of income spent on these expenses, we can divide the total amount spent by the net monthly income and then multiply by 100:

Percentage = (Total / Net income) x 100

Percentage = (4,680 / 7,800) x 100

Percentage = 0.6 x 100

Percentage = 60%

Therefore, the Sullivan family spends 60% of their net monthly income on food, clothing, and housing.

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The first statement is false and second statement is true.

a. In a reflection, pairs of corresponding points lie on parallel lines. False.

When we consider the reflection transformation, the corresponding points lie on a single line perpendicular to the reflecting line.

The reflecting line serves as the axis of reflection, and the corresponding points are equidistant from this line.

To illustrate this, imagine a triangle ABC and its reflected image A'B'C'. The corresponding points A and A' lie on a line perpendicular to the reflecting line.

The same applies to points B and B', as well as C and C'.

Therefore, the pairs of corresponding points do not lie on parallel lines but rather on lines perpendicular to the reflecting line.

b. In a translation, pairs of corresponding points are on parallel lines. True.

When we consider the translation transformation, all pairs of corresponding points lie on parallel lines.

A translation involves shifting all points in the same direction and distance, maintaining the same orientation between them.

Therefore, the corresponding points will form parallel lines.

For example, let's consider a square ABCD and its translated image A'B'C'D'.

The pairs of corresponding points, such as A and A', B and B', C and C', D and D', will lie on parallel lines, as the entire shape is shifted uniformly in one direction.

Hence the first statement is false and second statement is true.

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Answer:

the answer is i dont know

Step-by-step explanation:

just pretend that this is answer

Answer:

3/7

Step-by-step explanation:

Given set is {-18,-16,-14,-12,-10,-8,-6}

Probability = Number of favorable outcome / Number of possible outcomes

Favorable outcomes ={ -18, -12, -6}

probability of choosing a multiple of -6 = 3/7

The explicit formula for the sequence,

aₙ = 540(1/3)ⁿ⁻¹.

And the recursive formula for the sequence,

aₙ = aₙ₋₁(1/3).

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

Given:

540, 180, 60, 20, ...

The sequence is a geometric sequence.

First, we find the common ratio.

180/540 = 1/3

60/180 = 1/3

20/60 = 1/3

Hence, 1/3 is the common ratio

r = 1/3

So,

the explicit formula for the sequence,

aₙ = 540(1/3)ⁿ⁻¹.

And the recursive formula for the sequence,

aₙ = aₙ₋₁(1/3)

Therefore, the formulae are given above.

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Answer:

428.464

Step-by-step explanation:

If you divide any number by 1, the answer will come out the same as the number you are trying to divide.

Answer:

Really hope this helps

Step-by-step explanation:

Tom= £149.40

Ben= £522.90

Answer:

C 2:5

Step-by-step explanation:

The two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also commonly referred to as GP. The GP is generally represented in form a, ar, ar2.... where 'a' is the first term and 'r' is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio. Finite geometric progression contains a finite number of terms. It is the progression where the last term is defined. Infinite geometric progression contains an infinite number of terms. It is the progression where the last term is not defined.

Let the first term of the geometric progression be a and the common ratio be r.

The second term is less than the first by 36.

∴ a - ar = 36

⇒ a(1-r) = 36 --- (1)

The third term is greater than the fourth term by 324.

∴ ar² - ar³ = 324

⇒ ar²(1-r) = 324  --- (2)

Divide equation (2) by equation (1):

∴ r² = 9

⇒ r = ±3

Put r in the first equation:

⇒ a - ar = 36

⇒ a(1 - (±3) = 36

⇒ a = 36/4 or 36/-2

∴ a = 9 or -18

Similarly finding the other three terms:

ar = 9× -3 or -18×3  = -27 or -54

ar² = -27×-3 or -54×3 = -81 or -162

ar³ = -81×-3 or -162×3 = 243 or -486

Thus, the two possible sets of four numbers are (9,-27,81, -243) and (-18,-54,-162,-486).

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Answer:

Greater.

Step-by-step explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.

Answer:

The domain for f(x) is all real numbers greater than or equal to 2.

Step-by-step explanation:

Given function:

\(f(x)=2x^2+5 \sqrt{x-2}\)

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken:

\(\implies x-2\geq 0\)

Therefore:

\(\implies x-2+2\geq 0+2\)

\(\implies x\geq 2\)

Therefore, the domain of the given function is greater than or equal to 2.

Answer:

so you distrubute the 3 into the parenthesis and you then get 3n+15 is greater than or equal to 3n+8 then you subtract the 3n from the right side from the 3n on the left side and you are left with 15 is greater than or equal to 8

Step-by-step explanation:

Answer:

2 years late but its all reall numbers, good luck!

The product of (−21)(19)(−5) is 1995.

What is product?

In mathematics, the product is the result of multiplying two or more numbers or expressions together. The product is an important concept in mathematics and is used in many areas, including arithmetic, algebra, calculus, and geometry.

The problem asks us to find the product of (−21)(19)(−5). To solve this problem, we can multiply the three numbers together in any order because multiplication is associative.

So, let's multiply the numbers from left to right:

(−21)(19)(−5) = (−399)(−5)

We then simplify this expression by multiplying -399 and -5 together:

(−399)(−5) = 1995

Therefore, the product of (−21)(19)(−5) is -1995.

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Answer:

The coordinates are (2,1)

Step-by-step explanation:

We use the internal division formula here;

x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

Where;

m = 3 and n = 2

x1 = -4 , x2 = 6

y1 = -2 , y2 = 3

Substituting these values;

(x,y) = (2(-4) + 3(6))/(3 + 2) , (2(-2) + 3(3))/(2+3)

= (10/5 , 5/5)

= (2,1)

Answer:

b.) 9/g = 28.5

Step-by-step explanation:

a.) 9g = 28.5

b.) 9/g = 28.5

c.) 28.5 = 9 x g

d.) 28.5/9 = g

Total billing = $28.50

Rate = $9 per gigabyte

Calculate the additional gigabytes, g, that you used.

Additional gigabyte used, g = Total billing / Rate

g = $28.50 / $9

9g = 28.50

28.50 = 9 × g

g = 28.50 / 9

Option b.) 9/g = 28.5 is the incorrect way to calculate the additional gigabytes, g, that you used.

Answer:

9/g = 28.5

Step-by-step explanation:

It's attached to the image to show proof it's right

The Correlation Strength shown by the 3 graphs are respectively; 5. No correlation; 2. Strong Positive Correlation and 4. Weak positive correlation

A graph is said to have positive correlation if the relationship between two variables move in tandem in the same direction.

No correlation is also termed as zero correlation which means there is no relationship between the two variables.

Now, the first graph shows that there is no correlation at all between the x-values and y-values. Thus, It has No correlation.

The second graph shows strong positive correlation as the relationship between the x and y values are almost perfect.

The third graph shows weak positive correlation as the relationship between the variables though positive are very weak.

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Answer:

5.88 x 1012

Step-by-step explanation:

To write each of these numbers in decimal notation, you move the decimal point the same number of places as the exponent. If the exponent is positive, move the decimal point to the right. If the exponent is negative, move the decimal point to the left. If you start at the decimal of 5.88 and move it 12 spaces to the right, then you get 5,880,000,000,000 miles.

The number represented in scientific notation is 5.88×1013.

It is the way of writing a large number between 1 to 10 with a power of 10.

We have,

5,880,000,000,000 miles is equivalent to 1 light year.

We can convert this number to scientific notation by moving the decimal point 13 places to the left

(because there are 13 zeros in 5,880,000,000,000) and multiplying by 10 raised to the 13th power:

So,

= 5,880,000,000,000

= 5.88 × 10¹³

Therefore,

The number represented in scientific notation is 5.88×1013.

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Answer:

a. 8 gallons

b. (11-0.75t) gallons

Step-by-step explanation:

a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.

We proceed as follows;

Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours

Mathematically, that would be 0.75 * 4 = 3 gallon

Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.

That would be; 11 - 3 = 8 gallons

b. Like above, we want to know the amount of fuel left after t hours.

Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t

Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.

Mathematically, that would be 11- 0.75t

Answer:

Step-by-step explanation:

The volume of a cylinder:

New dimensions of the cake:

The volume of the bigger cake:

The ration of volumes is 12 : 1

The length of L of one "arch" of the cycloid that is the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire is 8R.

The parametric equations of cycloid are,

x(t) = R (t - sint)

y(t) = R (1 - cost)

Now differentiating the equations with respect to 't' we get,

x'(t) = R (1 - cost)

y'(t) = R sint

The length L of one arch of the cycloid is given by,

L = \(\int_a^b{\sqrt{(x'(t))^2+(y'(t))^2}}dt\)

Here since the curve is cycloid so a = 0 and b = \(2\pi\).

So,

L = \(\int_0^{2\pi}{\sqrt{(R(1-\cos t))^2+(R\sin t)^2}dt}\)

  = \(\int_0^{2\pi}{\sqrt{R^2(1-\cos t)^2+R^2\sin^2t}dt}\)

  = \(R\int_0^{2\pi}{\sqrt{1-2\cos t+\cos^2t+\sin^2t}dt}\)

  = \(R\int_0^{2\pi}{\sqrt{2-2\cos t}dt}~~~[\because \cos^2t+\sin^2t=1]\)

  = \(R\int_0^{2\pi}{\sqrt{2(1-\cos t)}dt}=R\int_0^{2\pi}{\sqrt{4\sin^2 \frac{t}{2}}dt}\)

  = \(2R\int_0^{2\pi}{\sin \frac{t}{2} dt}\)

  \(=2R\frac{[-\cos \frac{t}{2}]_0^{2\pi}}{\frac{1}{2}}=4R[-\cos\pi+\cos0]=8R\)

Hence the length L of an "arch" of the cycloid, that is, the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire is 8R.

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As the acceleration is a constant quantity, it's the same for all values of t, and therefore the motion is uniformly accelerated motion (UAM).

Thus, the particle is moving along a straight line.

Given, velocity function v(t) = 7 - 5t.

Here, a = -5
Since, acceleration is the derivative of velocity function.

Therefore,

acceleration, a(t)

= dv(t)/dt

= d/dt (7 - 5t)

= -5

On integrating, we get velocity function v(t) = 7 - 5t.

And, on integrating again we get distance function as the antiderivative of velocity function, that is,

s(t) = ∫v(t)dt

= ∫ (7 - 5t)dt

= 7t - (5/2)t² + C,

where C is the constant of integration.

Using the given initial condition s(0) = 5,

we have

5 = 7(0) - (5/2)(0)² + C

= C

On substituting C = 5,

we get s(t) = 7t - (5/2)t² + 5.

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The displacement of the particle from t = 0 to t = 2 is 4 units.

To find the displacement of the particle over the given time interval,

we need to integrate the velocity function with respect to time.

The velocity function is given as v(t) = 7 - 5t, where 0 < t < 2.

To find the displacement, we integrate v(t) with respect to t:

s(t) = ∫(v(t)) dt

s(t) = ∫(7 - 5t) dt

s(t) = 7t - (5/2)t² + C

To find the definite integral from t = 0 to t = 2, we substitute the upper and lower limits:

s(2) - s(0) = (7(2) - (5/2)(2)²) - (7(0) - (5/2)(0)²)

s(2) - s(0) = (14 - (5/2)(4)) - (0 - 0)

s(2) - s(0) = 14 - 10 - 0

s(2) - s(0) = 4

Therefore, the displacement of the particle from t = 0 to t = 2 is 4 units.

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Answer:

It was a little blurry but I think it might be B? Plz mark as brainliest if correct, thanks!