John can jog twice as fast as he can walk. He was able to jog the first 3.5 miles to
his grandmother's house, but then he tired and walked the remaining 3.5 miles. If the
total trip took 1.75 hours, then what was his average jogging speed?
miles per hour

The boat's displacement is approximately 84,016.8 metric tons.

To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:

26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)

Therefore, the boat's top speed is approximately 29.86 miles per hour.

To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:

93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)

Therefore, the boat's displacement is approximately 84,016.8 metric tons.

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There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.

Possible ways to make a sum of 2: 1

Possible ways to make a sum of 3: 2

Possible ways to make a sum of 4: 3

Possible ways to make a sum of 5: 4

Possible ways to make a sum of 6: 5

Possible ways to make a sum of 7: 6

Possible ways to make a sum of 8: 5

Possible ways to make a sum of 9: 4

Possible ways to make a sum of 10: 3

Possible ways to make a sum of 11: 2

Possible ways to make a sum of 12: 1

This means there are 21 ways to make a sum greater than 6.

21/36 ≈ 58.33%

There are 24 ways to make sums that are not divisible by 3 and not divisible by 6.   (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)

24/36 ≈ 66.67%

Answer:

2

Step-by-step explanation:

1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2

Answer: 266

Step-by-step explanation:

I = prt

p= 1900

r=.07

t=2

1900x.07x2=266

Value of system after 'x' years = [tex]3000*(0.85)^x[/tex]

The value of the computer after 3 years is $1842.375

The formula for an exponential function is f(x) =[tex]a^x[/tex], where 'x' is variable and 'a' is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given that, computer system values at $3000 decrease at a rate of 15% each year.

If the value decreases by 15%, it means that the new value is 85% of the old value.

new value = old value * (85/100)

new value = old value * 0.85

value in 1st year = $3000

value after 1st year = $3000 * 0.85

value after 2nd year = $3000 * 0.85 * 0.85

value after nth year = $3000 * [tex]0.85^n[/tex]

Value of the system after 3 years = $3000 * [tex]0.85^3[/tex]

= $3000 * 0.614125

= $1842.375

Therefore, The value of the computer system after 3 years  is $1842.375

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Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

Answer: A proper subset of a set A is a subset of A that is not equal to A

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = -3

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

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Answer: Width = 73 m

Step-by-step explanation:

Perimeter = Length(2) + Width(2)

330 - (92 x 2)

330 - 184 = 146

146 = Width of 2 sides

146/2 = 73 m

The sum of the first 8 terms is 13.5

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

9, 3, 1, 1/3, ...

Using the above as a guide, we have the following:

First term, a = 9

Common ratio, r = 1/3

The sum of GP (of n terms) is calculated as

Sum = Sn = a(r^n - 1) / (r - 1)

substitute the known values in the above equation, so, we have the following representation

Sum = 9 * ((1/3)^8 - 1)/((1/3) - 1)

Evaluate

Sum = 13.5

Hence, the sum is 13.5

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The number of widgets that Justin can make in 36 minutes is given as follows:

y = 36k.

In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

The constant is obtained as follows:

k = y/x.

For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:

y = 36k.

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The length of side LH is given as follows:

LH = 7 cm.

A translation happens when either a figure or a function are moved horizontally or vertically.

This is relevant because the side lengths remain constant.

The equivalent side to side LH is given as follows:

WZ = 7 cm.

Hence the length of side LH is given as follows:

LH = 7 cm.

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The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.

What's meant by rate?

Areas If the scale factor of the sides of two analogous polygons is m/ n

 also the rate of the areas is (m/n)^2.

Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.

It's given that, the rate of peripheries of two analogous quadrilateral is 2 4

 now,  

to find the rate of area, we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now rate of areas,

[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]

[tex]=\frac{2 \times 2}{4 \times 4}[/tex]

= 4/16

= 1/4

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26 is the value of a from the given figure.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of a from the figure.

∠D is 46 degrees.

AD is 28, AT is 37

CosD=Adjacent side/ Hypotenuse

Cos46=a/37

0.695=a/37

a=0.697×37

a=26

Hence, the value of a is 26

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Answer:

[tex]4x^{2} y^{3}[/tex]

Step-by-step explanation:

[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]

In the denominator, all the terms in the brackets or parenthesis will be squared:

= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]

Law of indices is applied:

                                                    [tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]

= [tex]4x^{4 - 2} y^{5 - 2}[/tex]

= [tex]4x^{2} y^{3}[/tex]

∴Option B

Answer:

B

Step-by-step explanation:

c=d*π

c=8*π

c=25.1 inches

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The length of side DF is 5 units.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar traingles are proportional .

Therefore, in the given triangles,

[tex]\frac{BA}{ED} =\frac{AC}{DF}[/tex]

[tex]\frac{6}{3} =\frac{10}{x} \\\\x=5[/tex]

Hence, the value of x = 5 units.

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1. The height of the cone is, 22.18 mm.

2. The slant height is, 28.14 mm.

3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

The volume of cone V = (1/3)πr²h

Given that,

The volume  = 8792 mm³

1. by using the formula to solve for h,

we get h = (3V)/(πr²).

Plugging in the values given,

we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.

Therefore, the height of the cone is approximately 22.18 mm.

2. it is known that, from the Pythagoras theorem

s² = h² + r²,

where s is the slant height, h is the height, and r is the radius.

Plugging in the values we found in part 1,

we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².

Taking the square root of both sides, we get s ≈ 28.14 mm.

Therefore, the slant height is approximately 28.14 mm.

3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.

Using the value we found in part 2,

the length of the slant height is approximately 28.14 mm.

Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.

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Answer:

Step-by-step explanation:

S+8=D

S+D equals 94.

94/2= 45+2=47

47-8=39

Sydney is 39

Answer:

43

Step-by-step explanation:

94-8= 86

86/2= 43

43+8= 51

a:43

prove it :

51+43= 94

Answer:

2 [tex]\frac{16}{17}[/tex] miles

Step-by-step explanation:

[tex]\frac{miles}{minutes}[/tex] = [tex]\frac{miles}{minutes}[/tex]

[tex]\frac{1 1/4}{8 1/2}[/tex] = [tex]\frac{x}{20}[/tex]

1 [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{4}{4}[/tex] + [tex]\frac{1}{4}[/tex]   (1 = [tex]\frac{4}{4}[/tex] )

8 [tex]\frac{1}{2}[/tex] is the same as [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{17}{2}[/tex]   (1 = [tex]\frac{2}{2}[/tex])

[tex]\frac{\frac{5}{4} }{\frac{17}{2} }[/tex] = [tex]\frac{x}{20}[/tex]

[tex]\frac{17}{2}[/tex] x = 20  multiply both sides by [tex]\frac{2}{17}[/tex]

[tex]\frac{2}{17}[/tex] [tex](\frac{17}{2})[/tex]x = [tex]\frac{2}{17}[/tex][tex](\frac{20}{1})[/tex]

x = [tex]\frac{40}{17}[/tex]

[tex]\frac{5}{4}[/tex] [tex](\frac{40}{17})[/tex] = x

[tex]\frac{50}{17}[/tex] or 2 [tex]\frac{16}{17}[/tex]

The triangle's perimeter is roughly 25.29 cm.

The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.

Let's call the right triangle's shorter leg "x" for short.

The longer leg is then 5 cm longer than x, or x + 5, according to the situation.

The hypotenuse measures x + 10 cm longer than x.

By the Pythagorean theorem, we know that:

x² + (x+5)² = (x+10)²

Expanding and simplifying this equation gives:

2x² + 10x - 75 = 0

Dividing both sides by 2 gives:

x² + 5x - 37.5 = 0

We can find the value of x by using the quadratic formula:

x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2

x = (-5 ± sqrt(175)) / 2

x ≈ -8.68 or x ≈ 3.43

Since x represents a length, we must choose the positive solution x = 3.43 cm.

Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:

3.43 + 8.43 + 13.43 = 25.29 cm

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The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The radius and height of the cone and the cylinder are the same. Then the ratio of the volume of the cylinder to the volume of the cone is 3. Then we have

(Volume of the cylinder) / (Volume of the Cone) = 3

Volume of the cylinder  / 222 = 3

Volume of the cylinder = 666 cubic cm

The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

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The number of bees that will equal the mass of a single moose is 5 × 10⁶.

Given the data in the question;

To determine the number of bees that will equal the mass of a single moose.

Let the number be represented by x.

Hence;

Number of bees × mass of bee = mass of moose

n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³

Divide both sides by ( 2.5 × 10⁻⁴ ).

n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )

n = 1250 / 0.00025

n = 5,000,000

Therefore, the number of bees is 5,000,000.

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Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

Step-by-step explanation:

The inequality on the graph is written as:

-4 < x ≤ 5

Here we have an inequality graphed on a number line.

First, we can see that we have an open circle at x = -4 and then the line goes to the right.

That means that the value of x must be larger than -4, so we can start by writting:

-4 < x

Then we have a closed circle at x = 5.

That means that x can be smaller or equal to 5, then:

x ≤ 5

Then the inequality is:

-4 < x ≤ 5

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In right triangle ABC, the value of x is equal to 0.06.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Since the angle formed by side A is a right triangle, we have the following complementary angles;

C + B = 90

sin(C) = cos(B)

x + 0.26 = 3x + 0.14

3x - x = 0.26 - 0.14

2x = 0.12

x = 0.12/2

x = 0.06

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