Speed, Time, and Dis
1 a. Noah rides his bike with a constant
speed of 18 km/h. How long will he
take to travel a distance of
54 kilometers?

Answer:

No. All the lengths will not be the same.

Step-by-step explanation:

Martha wants to make four necklaces that are the same length. She asked her friends to cut the string for the necklaces 15 paper clips long.

We are asked whether all the four lengths will be of the same length or not.

If Martha uses the paper clips to measure the lengths of the cut pieces of strings, then all the lengths will not be the same because 15 is not divisible by 4.

The lengths maybe 4, 4, 4, and 3 paper clips of lengths. (Answer)

Length of each string is 3.75 paper clips

Number of neckless = 4

Length of string = 15 paper clips

Length of each string

Length of each string = Length of string / Number of neckless

Length of each string = 15 / 4

Length of each string = 3.75 paper clips

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total vol. = 24

If length x base x height = vol. of cuboid

then,

vol. of cuboid = width

base x height

24 / (4 x 2) =

24/8=

3ft

Answer: $57.77

Step-by-step explanation:

3 x 12.50 = 37.5 + 20 = 57.5

57.5- 3 = 54.5

54.5 x .06 = 3.27

54.5 + 3.27 = $57.77 is the answer

The value of log base 12 of y² is evaluated by using the power rule of logarithms. Given that log base 12y equals 16, the value of log base 12 of y² is calculated to be 32.

The student asked to evaluate log base 12 of y², given that log base 12y = 16. From the given information, we have:

log12(y) = 16

Using the power rule of logarithms, which states that logb(xy) = y. logb(x), we can express the asked expression log12(y²) as:

log12(y²) = 2 . log12(y)

Since we are given that log12(y) = 16, we can substitute this value into our previous equation:

log12(y²) = 2 . 16 = 32.

Therefore, the value of log12(y²) is 32.

Answer:

The value of x is 8

Step-by-step explanation:

In the figure below,

The alternate exterior angles are  1 and 2

Alternate Exterior Angles are a pair of angles that lie on the  outer side of each of those two lines but on opposite sides of the transversal and they are equal

Also  angle 2 and 3 are adjacent and supplementary angle and their sum is equal to 180 degrees

Given that

[tex]\angle 1 = (4x + 28)^{\circ}[/tex]

[tex]\angle 3 = (14x + 8)^{\circ}[/tex]

Now we know that

[tex]\angle 2 + \angle 3 = 180 ^{\circ}[/tex]

[tex]\angle 2 +(14x+8) = 180[/tex]

[tex]\angle 2 = 180 - 14x -8[/tex]

[tex]\angle 2 = 172 - 14x[/tex]

We also know that

[tex]\angle 1 = \angle 2[/tex]

[tex]4x + 28 = 172 -14x[/tex]

[tex]4x + 14x = 172 - 28[/tex]

[tex]18x = 144[/tex]

[tex]x =\frac{144}{18}[/tex]

x = 8

Now

[tex]\angle 1 = (4x+28)^{\circ} = (4(8) +28)^{\circ} = (32 +28)^{\circ} =(60)^{\circ}[/tex]

[tex]\angle 3= (14x+8)^{\circ} = (14(8) +8)^{\circ} = (112 +8)^{\circ} =(120)^{\circ}[/tex]

Answer:

The value of x is 8

Step-by-step explanation:

Answer:

The owner can use between 5 and 20 HCF to stay in the conservation range

Step-by-step explanation:

Let's calculate the number of HCF, this way:

Lower value = (31.32 - 24.72)/1.32 = 6.60/1.32 = 5

Upper value = (52.12 - 24.72)/1.32 = 27.4/1.32 = 20.76 = 20 as truncated value

The owner can use between 5 and 20 HCF to stay in the conservation range

The owner can use between 5 and 20 hcf to stay within the conservation range.

To find the range for the number of hcf the owner can use, we need to subtract the base cost from the maximum and minimum bill amounts. The base cost is $24.72, so subtracting this from the maximum bill amount of $52.12 gives us $27.40. Similarly, subtracting the base cost from the minimum bill amount of $31.32 gives us $6.60. In order to determine the maximum and minimum number of hcf, we divide these amounts by the additional cost per hcf, which is $1.32.

The maximum number of hcf would be $27.40 divided by $1.32, which is approximately 20 hcf. The minimum number of hcf would be $6.60 divided by $1.32, which is approximately 5 hcf.

Therefore, the owner can use between 5 and 20 hcf to stay within the conservation range.

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Answer:

The answer is 3

Step-by-step explanation:

i) -4 - (-7)   = -4 + 7 = 7 - 4 = 3   .... since  (minus) [tex]\times[/tex] (minus) = plus

Answer:

radius = 6 cm

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex] πr³ ← r is the radius

Given V = 288π, then

[tex]\frac{4}{3}[/tex] πr³ = 288π

Multiply both sides by 3 to clear the fraction

4πr³ = 864π ( divide both sides by 4π )

r³ = 216 ( take the cube root of both sides )

r = [tex]\sqrt[3]{216}[/tex] = 6

Thus the radius of the sphere is 6 cm

To find the sphere's radius from its given volume of 288pi cm^3, we use the volume formula V = (4/3) π r³ and solve for r, resulting in a radius of 6 cm.

The student is asking for the radius of a sphere given its volume, which is 288pi cm³. To find the radius, we need to use the formula for the volume of a sphere:

V = (4/3) π r³

Where V is the volume and r is the radius. We can solve for r by rearranging the formula:

r = √[3V / (4π)]

In this case, substituting the given volume into the equation:

r = √[3(288π) / (4π)]

r = √[864π / (4π)]

r = √[216]

The radius of the sphere is 6 cm.

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Answer:

The value of A is [tex](-\infty, 0) \cup(0, \infty)[/tex]

Step-by-step explanation:

Given:

[tex]V = A (t- 0.05t^2)[/tex]

When velocity V= 0

we have

[tex]A (t- 0.05t^2) = 0[/tex]

[tex](t- 0.05t^2) = 0[/tex]

[tex]t = 0.05t^2[/tex]

t =0 , t = [tex]\frac{1}{0.05}[/tex]

t = 0 , t = 20

So when we draw a graph,The resulting graph will be  a quadratic graph.

[tex]\frac{dv}{dt} = A[1 - 0.1t][/tex]

[tex]\frac{dv}{dt} = 0[/tex]

t=10 sec

At t=10, the velocity will be

[tex]v(10) = [10 -0.05(10)^2][/tex]

[tex]v(10) = [10 -5][/tex]

[tex]v(10) = 5A[/tex]

But according to the question A is not dependent on t

So A can be any  value other than zero

Answer:

Step-by-step explanation:

Answer: { 2 , 7 }

Step-by-step explanation:

The intersection of a set is what the sets have in common. From the given sets , the numbers common to the two are 2 and 7 , so the intersection of the sets will be { 2 , 7 }

Answer:

He should buy a 50 inch TV

Step-by-step explanation:

Using Pythagorean theorem the TV cabinet has a diagonal of :

[tex]\sqrt{30^{2} + 40^{2} } = 50[/tex]

Answer:

5/2

Step-by-step explanation:

3x/5=3/2

x=(3/2)/(3/5)

x=(3/2)(5/3)

x=5/2

Answer:  identity is subtraction property of equality equation is x + 8 = 6

Substitution Property of Equality; x + 8 = 6

Take the equation x + 8 = 6. subtract 8 from both sides using the subtraction property of equality x + 8 - 8 = 6 - 8 simplify x + 0 = -2 x = -2

The Addition Property of Equality and the equation x + 6 = 8 are the property and equation that satisfy the statement 'The solution of an equation is x = –2'. This is because when you subtract 6 from both sides of the equation, x equals -2.

To find the property and equation that fits the statement 'The solution of an equation is x = –2', we need to understand the basic properties of equality and apply those in this context.

Following the statement, it seems that the Addition Property of Equality fits the best here. The Addition Property of Equality states that when we add the same number to both sides of an equation, the equation remains balanced and the solution is the same. Now, if we think of an equation 'x + 6 = 8', and solve it using the Addition Property by subtracting 6 from both sides, we get the solution x = -2.

That means the property that satisfies the statement is Addition Property of Equality and the equation that satisfies the statement is x + 6 = 8.

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Answer:

Money Jevon would be having = $15

Money Angie would be having = $30

Money Kenny would be having = $35

Step-by-step explanation:

Given:

Angie has twice as much money as Jevon

Kenny has $5 more than Angie.

The sum of their treasure = $80

To find how much money does each of them have.

Solution:

Let Jevon has money in dollars = [tex]x[/tex]

Angie having twice as much money as Jevon would have in dollars = [tex]2x[/tex]

Kenny having $5 more than Angie would have in dollars = [tex]2x+5[/tex]

The sum of their money will be given as:

⇒ [tex]x+2x+2x+5[/tex]

Combining like terms.

⇒ [tex]5x+5[/tex]

The sum of their treasure = $80

So, the equation to find [tex]x[/tex] would be given as:

[tex]5x+5=80[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 5.

[tex]5x+5-5=80-5[/tex]

[tex]5x=75[/tex]

Dividing both sides by 5.

[tex]\frac{5x}{5}=\frac{75}{5}[/tex]

∴ [tex]x=15[/tex]

Thus,

Jevon has = $15

Angie has = [tex]2\times \$15[/tex] = $30

Kenny has =  [tex]\$30+\$5[/tex] = $35

Final answer:

The house will be worth $153,420 when it is 16 years old, calculated by finding the annual increase in value from the given data and projecting this increase over the relevant time period.

Explanation:

To calculate the worth of the house when it is 16 years old, we need to establish the rate at which the house's value is increasing over time, based on the information given for its value at 2 years and at 7 years. The house is valued at $125,000 when it is 2 years old and $135,150 when it is 7 years old, showing an increase of $10,150 over 5 years.

First, we find the annual increase in value by dividing the total increase by the number of years:

Annual increase = $10,150 / 5 = $2,030.

Next, we predict the value when the house is 16 years old by multiplying the annual increase by the number of years from the starting point (2 years old) to 16 years old:

14 years (from year 2 to year 16) × $2,030 annual increase = $28,420 increase since year 2.

Finally, we add this increase to the original value at year 2:

Projected Value at Year 16 = $125,000 + $28,420 = $153,420.

Hence, according to the model, the house will be worth $153,420 when it is 16 years old.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$410000\\ r=rate\to 3.85\%\to \frac{3.85}{100}\dotfill &0.0385\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(410000)(0.0385)(1)\implies I=15785[/tex]

Final answer:

The perimeter of the square defined by the city block is 616 meters.

Explanation:

In order to find the perimeter of the square block, we need to know the length of each side. The question states that each side of the block is 154 m, so we can use this information to calculate the perimeter. The perimeter of a square is equal to four times the length of one side, so in this case it would be 4 * 154 m = 616 m. Therefore, the perimeter of the square defined by this city block is 616 meters.

Answer:

Last one

Step-by-step explanation:

Imagine it as a mirror or like a paper folding in half, then figure out the direction it shifts.

Answer:

[tex]x\leq 36[/tex]

The solution for [tex]x[/tex] is all real numbers less that or equal to 36.

Step-by-step explanation:

Given expression:

[tex]\frac{1}{2}x\leq18[/tex]

To find the solution for [tex]x[/tex]

Solution:

In order to solve for [tex]x[/tex] , we will make sure to isolate the unknown variable [tex]x[/tex] on left side alone by doing math operations on both sides of the inequality.

We have:

[tex]\frac{1}{2}x\leq18[/tex]

Multiplying both sides by 2.

[tex]2.\frac{1}{2}x\leq18\times 2[/tex]

The 2 on left side will cancel each other leaving [tex]x[/tex] alone.

Thus, we have:

[tex]x\leq 36[/tex]

Thus, solution for [tex]x[/tex] is all real numbers less that or equal to 36.

Answer:

D

Step-by-step explanation:

The correct description for the polynomial [tex]-5x^{2} -3x+3[/tex] is quadratic trinomial.

Explanation:

Option a: Quartic binomial

A polynomial with degree 4 is said to be quartic polynomial. Also, if the polynomial contains two terms then it is binomial.

Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is not quartic binomial.

Option b: Quadratic binomial

A polynomial with degree 2 is said to be quadratic polynomial. Also, if the polynomial contains two terms then it is binomial.

Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is not quadratic binomial.

Option c: Quadratic trinomial

A polynomial with degree 2 is said to be quadratic polynomial. Also, if the polynomial contains three terms then it is binomial.

Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is a quadratic trinomial.

Option d: Cubic binomial

A polynomial with degree 3 is said to be cubic polynomial. Also, if the polynomial contains two terms then it is binomial.

Hence, the polynomial [tex]-5x^{2} -3x+3[/tex] is a cubic binomial.

Thus, the polynomial [tex]-5x^{2} -3x+3[/tex] is quadratic trinomial.

Answer:

quadratic trinomial

Step-by-step explanation:

Answer:

3.33 or 10/3

Step-by-step explanation:

simplify by dividing 40/12 by 4:

10/3 or 3.33

The value of the answer on dividing 83.40 by 12 is 6.95, i.e. 83.40 ÷ 12 = 6.95.

It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

83.40 divided by 12,

The above expression can be written as,

83.40 ÷ 12

Divide the term 83 by 12. You get a quotient of 6 and a reminder of 11 put the dot and then take the value of 4 down, the number will be 114 divided by 12. You will get 9 quotients and 6 as a reminder, Then drop the value 0 and the new number is 60, divide 60 by 12 you will get question 5 and the remainder zero.

Thus, 83.40 ÷ 12 = 6.95.

To know more about division:

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The fraction [tex]\frac{13}{50}[/tex] is spent on federal income taxes.

Step-by-step explanation:

Given,

Combined income of parents = $20,000

Amount paid in federal income taxes = $5200

Fraction = [tex]\frac{Amount\ paid\ in\ taxes}{Combined\ income}[/tex]

Fraction spent on taxes =  [tex]\frac{5200}{20000}[/tex]

Fraction spent on taxes = [tex]\frac{52}{200}[/tex]

Fraction spent on taxes = [tex]\frac{13}{50}[/tex]

The fraction [tex]\frac{13}{50}[/tex] is spent on federal income taxes.

Keywords: fraction, division

Learn more about fractions at:

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Answer:

Step-by-step explanation:

You already know the area, so just reverse the steps. Example: 200ft divided by the length which is 16ft equals 12.5 feet

Answer:

The number that occurs most often in a set of numbers

in this case, the number 100 occurs more than any other number in the set.  This means that the mode for this set of data is 100.

Answer:

100

Step-by-step explanation:

Mode is the number that appears most often

Hence

In the given set of numbers

The mode is 100

Answer:

y = 5x + 17

Last choice

Step-by-step explanation:

The equation for a line can be written in the form y = mx + b. (This is called slope-intercept form).

"x" and "y" mean points on the line.

"m" means the slope of the line, which is how steep the line is.

"b" means the y-intercept, which is when the line hits the y-axis.

To write an equation in slope-intercept form, we need the slope and y-intercept.

We know the slope needs to be 5.

m = 5

We know one point on the line, (-4, -3). Points are written (x, y), so:

x = -4

y = -3

Substitute the numbers we know for "m", "x" and "y" into the equation for a line. Then, we can isolate 'b' to know what it equals.

y = mx + b

-3 = (5)(-4) + b       Multiply to simplify

-3 = -20 + b        Start isolating 'b'

-3 + 20 = -20 + 20 + b     Add 20 to both sides to cancel out on the right.

-3 + 20 = b     Solve the left side.

17 = b      Answer

b = 17    Put variable on left side for standard formatting

Now that we know m = 5 and b = 17, rewrite the equation in the form y = mx + b.

y = 5x + 17

Answer:

The temperature next morning was - 19.1 degrees

Step-by-step explanation:

High temperature in Fairbanks, Alaska = 12.2 degrees

Temperature that night = 12.2 - 48.4

Temperature that night = -36.2 degrees

Temperature next morning = -36.2 + 17.1

Temperature next morning = -19.1 degrees

The temperature next morning was - 19.1 degrees

You weren't being specific so I searched up the question.

The correct answer is:

A. 1/169 - The probability of drawing a king followed by a queen with a replacement.

B.1/442 - The probability of drawing a red ace followed by another red ace without replacement.

C.4/442 -  The probability of drawing a 3 or 5 followed by 4 or 6, with replacement.

D.1/52 - The probability of drawing a spade followed by a jack of ant color with replacement.

Keep in mind this is not my answer since I got it from somebody else.

Answer:

Refer to the picture bellow

Step-by-step explanation:

Answer:

PT=57

Step-by-step explanation:

If PT=7x+8 and TQ=9x-6 qnd we have that T is the midpoint of PQ.

Since T is the midpoint of PQ, [tex]PT=TQ[/tex]

We substitute into the equation to get:

[tex]7x+8=9x-6[/tex]

Group the similar terms to get:

[tex]8+6=9x-7x[/tex]

We simplify now to get:

[tex]14=2x[/tex]

Divide through by 2 to get:

[tex]x=7[/tex]

PT=7*7+8=49+8=57