4. The area of a rectangle is x² + 5x - 24. Which of the following could be one of the dimensions?
O(x-8)
O(x-6)
O(x+8)
O(x-4)

Answer:

57 kg

Step-by-step explanation:

5% less means it weighs 95% of what it used to weigh

95% is .95 in decimal

.95 * 60 = 57 kg

circumference of the mirror = 175.84 cm

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

The circumference and area of a circle can be found as follows:

circumference of the mirror = 2πr

circumference of the mirror = 2 × 3.14 × 28 = 175.84 cm

area of the mirror = πr²

area of the mirror = 3.14 × 28²

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

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Answer:

The answer options appear garbled.  If A is 4/9, then this is equal to 2/3.  The others I can't see/understand.

Step-by-step explanation:

Answer:

D. Both factors are positive, so the product will be positive.​

Answer: B

Step-by-step explanation:

Using the distance formula, we get the height is [tex]4\sqrt{2}[/tex].

Similarly, we get the base is [tex]6\sqrt{2}[/tex].

So, the area is [tex]\frac{1}{2}(4\sqrt{2})(6\sqrt{2})=24[/tex]

4.6 moles in 187 grams of magnesium oxide (mgo).

To solve ,

             number of moles is equals to the mass in grams divided by RFM

                 RFM=16+24.3=40.3

                            =187/40.3

                             =4.6 moles of MgO

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Distributive property states that A × (B + C) = AB + AC. are always equal.

According to the statement

we have to explain the distributive property over multiplication.

Distributive property is the multiplication property.

According to this property, it generalizes the Distributive Law and it tells us that the an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

It means that From distributive property

A × (B + C) = AB + AC.

These are always equal with each other.

Now we will explain with an example,

Let A = 2, B = 3 and C = 4

Then

2 × (3 + 4) = 2(3) + 2(4).

2 × (7) = 2(3) + 2(4).

14 = 6 + 8.

14 = 14.

It proves that the A × (B + C) = AB + AC.

So, Distributive property states that A × (B + C) = AB + AC. are always equal.

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Answer:

7.5 m           457.5[tex]\pi[/tex] [tex]m^{2}[/tex]

Step-by-step explanation:

First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.

The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = [tex]\frac{1}{3} \pi r^{2}h[/tex].

Original Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] = [tex]\frac{1}{3} \pi *7.5^{2}*50[/tex] = 937.5[tex]\pi[/tex]

Smaller Cone = [tex]\frac{1}{3} \pi r^{2}h[/tex] =  [tex]\frac{1}{3} \pi *6^{2}*40[/tex] = 480[tex]\pi[/tex]

Frustum = 937.5[tex]\pi[/tex] - 480[tex]\pi[/tex] = 457.5[tex]\pi[/tex]

Answer:

1/a + 1/b + 1/c = 1 , a,b,c is nonzero

Step-by-step explanation:

bc +ac +ab /abc = 1

bc + ac + ab = abc

a = b = c = 1

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is [tex]2w+6[/tex].

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

[tex]A=w(2w+6)[/tex]

We can also substitute 40 in for A as it's given in the question.

[tex]40 = w(2w+6)[/tex]

Distributing w by multiplying it by both terms in the parentheses, we get

[tex]40 = 2w^2+6w[/tex]

We can make the equation simpler by dividing both sides by 2.

[tex]20 = w^2+3w[/tex]

Subtracting both sides by 20 will make the left-hand side 0.

[tex]0=w^2+3w-20[/tex]

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

[tex]w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}[/tex]

[tex]w= \frac{-3\pm\sqrt{9+80}}{2}[/tex]

[tex]w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}[/tex]

Since the second solution results in a negative number, it cannot be the length of w.

[tex]w=\frac{-3+\sqrt{89}}{2}\approx3.217[/tex]

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

[tex]l=2(3.217)+6[/tex]

[tex]l=12.434[/tex]

The length of this rectangle is 12.434 cm.

A cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.

A cross-section parallel to the base will be a square.

One perpendicular to the base will be a trapezoid, or if it passes through the vertex of the pyramid, a triangle.

Hence, a cross-section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base square, triangle, and, trapezoid.

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The correct answer is 7/12.

What is probability?

Let A = Getting multiple of  on the first one

     B = A total of  for both roll

P (A U B) = P(A) + P(B) - P(A ∩ B)

               [tex]\frac{18}{36} + \frac{5}{36} - \frac{2}{36} \\\\ = \frac{21}{36} \\[/tex]

                [tex]\frac{7}{12}[/tex]

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Answer: -4, 0, 2

Step-by-step explanation:

The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].

Answer:

-1728:512

Step-by-step explanation:

(-12)³ = -1728

8³ = 512

ratio is -1728:512

Answer:

Please see attachment.

Step-by-step explanation:

Remember, the 1/4x is the slope, and the -4 is the y-intercept.

Please see attachment for the graph.

Hope this helps!

1. The time taken for the water to fall that much is 0.2 s

2. The initial speed of the water is 4 m/s

h = ½gt²

0.2 = ½ × 9.8 × t²

0.2 = 4.9 × t²

Divide both side by 4.9

t² = 0.2 / 4.9

Take the square root of both side

t = √(0.2 / 4.9)

t = 0.2 s

s = ut

Divide both sides by t

u = s / t

u = 0.8 / 0.2

u = 4 m/s

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The solution of the equation are as follows:

x = 6 and y = -5

4x + 5y = -1

-5x - 8y = 10

Therefore,

20x + 25y = -5

-20x - 32y = 40

-7y = 35

y = -5

Hence,

4x + 5(-5) = -1

4x - 25 = -1

4x = -1 + 25

4x = 24

x = 24 / 4

x = 6

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Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3

=[tex]\frac{10!}{7!3!}[/tex]

= [tex]\frac{8.9.10}{3!}[/tex]

= 120

Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.

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Hello,

[tex] \frac{32 {x}^{8} }{8x {}^{32} } = \frac{4 \times 8 \times x {}^{8} }{8x {}^{32} } = \frac{4x {}^{8} }{x {}^{32} } = 4x { }^{8 - 32} = 4x {}^{ - 24} [/tex]

Answer:

[tex] \red{4 {x}^{ - 24} }[/tex]

Step-by-step explanation:

We know that,

[tex] {a}^{m} \times {a}^{m} = {a}^{m + n} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \: \: \: \: \: \: \: \: \: \: \: \\ \\ ({a}^{m})^{n} = {a}^{mn} \: \: \: \: \: \: \: \: \: \: [/tex]

Now using the above knowledge let us solve the sum.

[tex] \frac{32 {x}^{8} }{8 {x}^{32} } \\ ( \frac{32}{8} ) \times ( \frac{ {x}^{8} }{ {x}^{32} } ) \\ 4 \times {x}^{8 - 32} \\ 4 \times {x}^{ - 24} \\ = 4 {x}^{ - 24} [/tex]

Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:

A. 72 < x < 88.5.

It states that, for a normally distributed random variable:

The percentage that 978 is of 1200 is:

978/1200 x 100% = 81.5%.

Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:

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In Bayes Theorem, apart from the already starting information, some new information so that you can update or transform the original probabilities so you now have better information.

What is Bayes Theorem?

The Bayes' theorem was named after Thomas Bayes and it is used in probability theory and statistics as one of the fundamental theorems. It estimates the likelihood of an event based on knowledge of circumstances that might be connected to it in the past.

The Formula for Bayes' Theorem

The Bayes' theorem is given as,

P(A|B) = P(A).P(B|A) / P(B)

Here, for two events A and B,

P(A|B) is the probability for likelihood of A when B is true

P(B|A) is probability for likelihood of B when A is true

P(A) is the independent probability of event A

P(B) is the independent probability of event B

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Answer:

Step-by-step explanation:

Let the fraction be x/y.

According to question we have the following equations.

The denominator of a fraction exceeds numerator by 3:

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

Change the fraction as below and solve for y:

Find the value of x using the first equation:

The fraction is:

Answer:

Original fraction = ⁴/₇

Step-by-step explanation:

Numerator:  top of the fraction

Denominator: bottom of a fraction

Let x be the original numerator.

If the denominator of a fraction exceeds the numerator by 3:

[tex]\implies \dfrac{x}{x+3}[/tex]

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

[tex]\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}[/tex]

Cross multiply:

[tex]\implies 2x(3x+9)=2x(x+17)[/tex]

Divide both sides by 2x:

[tex]\implies 3x+9=x+17[/tex]

Subtract x from both sides:

[tex]\implies 2x+9=17[/tex]

Subtract 9 from both sides:

[tex]\implies 2x=8[/tex]

Divide both sides by 2:

[tex]\implies x=4[/tex]

Substitute the found value of x into the original fraction:

[tex]\implies \dfrac{4}{4+3}=\dfrac{4}{7}[/tex]

Therefore, the original fraction is ⁴/₇.

Step-by-step explanation:

x³ - x² - 24x - 36

factors of -36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and negative equivalents.

1 - 1 - 24 - 36 != 0

8 - 4 - 48 - 36 != 0

27 - 9 - 72 - 36 != 0

64 - 16 - 96 - 36 != 0

216 - 36 - 144 - 36 = 0

So one factor is 6

x = 6

(x - 6) = 0

x²(x - 6) = x³ - 6x²

5x(x - 6) = 5x² - 30x

6(x - 6) = 6x - 36

x³ - 6x² + 5x² - 30x + 6x - 36

(x - 6)(x² + 5x + 6)

(x - 6)(x² + 3x + 2x + 6)

(x - 6)(x(x + 3) + 2(x + 3))

(x - 6)(x + 3)(x + 2)

x - 6 = 0

x = 6

x + 3 = 0

x = -3

x + 2 = 0

x = -2

x = -2, -3, 6.

One is the product of the other 2 as -2 x -3 = 6.

Graphic proof is shown above or below in the image

Answer:

1)3×-8

-24

Step-by-step explanation:

2)bshejejnenenejejkejehrh

Using a linear function, the inequality is given by: 69.5 + 5x < 90.

The solution is: x < 4.1.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the cost of using x gigabytes is:

C(x) = 69.5 + 5x.

The cost has to be under 90, hence the inequality is:

C(x) < 90

69.5 + 5x < 90.

Then the solution is:

5x < 90 - 69.5.

x < 20.5/5

x < 4.1.

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Answer:

Inequality: 5x+35<50

Answer: x<3

Step-by-step explanation:

The 95% confidence interval based on the same data is 5.15 < μ < 6.05

Because it has a longer interval, the 95 percent confidence interval offers more details.

The likelihood that a parameter will fall between two values near the mean is shown by a confidence interval.

Confidence intervals quantify how certain or uncertain a sampling technique is.

Confidence intervals are used by statisticians to gauge the degree of uncertainty in a sample variable.

The 90% confidence interval is given by:

Mean - 1.645(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.645(S.D./[tex]\sqrt{n}[/tex])

2μ = 5.22 + 5.98 = 11.2

μ = 11.2 / 2 = 5.6

Thus,

5.6 - 5.22 = 1.645(S.D./[tex]\sqrt{n}[/tex]) = 0.38

S.D./[tex]\sqrt{n}[/tex] = 0.38 / 1.645 = 0.231

The 95% confidence interval is given by:

Mean - 1.96(S.D./[tex]\sqrt{n}[/tex]) < μ < Mean + 1.96(S.D./[tex]\sqrt{n}[/tex])

=5.6 - 1.96(0.231) < μ < 5.6 + 1.96(0.231)

= 5.6 - 0.4528 < μ < 5.6 + 0.4528

= 5.15 < μ < 6.05

The 95% confidence interval provides more information because it has a larger interval.

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Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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