By taking the quotient between distance and time, we conclude that her speed is 108.8 miles per hour.
How to find her speed?
Here we will use the next relation:
speed = distance/time.
Here we know that Mackenzie drove 68 miles in (1 + 3/5) hours, then:
distance = 68 mi
time = (1 + 3/5) hours = (8/5) hours.
Then the speed will be:
speed = 68mi/(8/5) hours. = 68*(8/5) mi/h = 108.8 mi/h
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Which describes a line passing through (3,3) that is perpendicular to the line described by y=3/5x+2 ?
Given:
Point (3,3)
The equation of the line,
[tex]y=\frac{3}{5}x+2[/tex]To find the equation of the line that passes through (3,3) and is perpendicular to the line:
The perpendicular slope is,
[tex]m=-\frac{5}{3}[/tex]Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{5}{3}(x-3) \\ y=-\frac{5}{3}x+5+3 \\ y=-\frac{5}{3}x+8 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-\frac{5}{3}x+8[/tex]Let us find the intercepts.
When x=0, we get y=8
So, the y-intercept is (0,8).
When y=0, we get
[tex]\begin{gathered} -\frac{5}{3}x+8=0 \\ \frac{5}{3}x=8 \\ x=\frac{24}{5} \\ x=4.8 \end{gathered}[/tex]So, the x-intercept is (4.8,0).
Hence, the correct option which satisfies the equation of the line is D (last option).
The ice skating rink charges $5 for a skate rental and $3 for every hour that you skate. What would be the equation you would use to determine how much you would need to pay?
If we use the variable t to represent the number of hours skating, the fixed price is $5 and the variable price is $3 per hour, that is, we have a variable cost of 3t.
So the final cost (variable C) is the sum of the fixed and variable costs:
[tex]C=5+3t[/tex]Q1 of the numbers 5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Answer
Q1 = 10
Explanation
To ontain the Q1, we need to first make sure the numbers are arranged in ascending or descending order.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Q1 is the number that occurs at the (N + 1)/4 position for the distribution.
N = Number of variables = 11
Q1 = (N + 1)/4
Q1 = (11 + 1)/4 = (12/4) = 3rd variable.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
The 3rd variable = 10
Hope this Helps!!!
Answer:
10
Step-by-step explanation:
i'm drinking boba and am to lazy to explain.
Which statements describe one of the transformations performed on f(x) = x?to create g(x) - 3(x + 5)2 - 2? Choose all that apply.DA. A translation of 2 units to the leftI B. A vertical stretch with a scale factor of 3O C. A vertical stretch with a scale factor of3O D. A translation of 5 units to the left
Solution:
The Function transformation of f(x) is:
[tex]g(x)=f(x+c)+d[/tex]If c > 0, then the graph shift left f(x+c).
If c<0, then the graph shift right f(x-c)
If d > 0, then the graph shift up f(x) +d
If d < 0, then the graph shift down f(x) -d
When the given equation is:
[tex]f(x)=x^2[/tex]The transformation equation is given:
[tex]g(x)=3(x+5)^2-2[/tex]Then, the graph shifts down 2 units and shifts left 5 units.
Also, the vertical stretch with a scale factor 3.
Therefore, the correct options are B and D.
Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?
Compound interest formula:
[tex]A\text{ = }P(1+i)^n[/tex]where:
A is the final amount, here = $250,000
P is the principal amount
i is the interest rate per year (in decimal form), here = 0.085
n is the number of years invested, here = 14
Replacing into the equation and solving for P, we get:
[tex]250000=P(1+0.085)^{14}[/tex][tex]\frac{250000}{1.085^{14}}=P[/tex]
P = $79,785.5
B) Use the quadratic formula to find the roots of each quadratic function.
Which of the following is the solution to the compound inequality below?5 + x>3or6x +1 -29O A. x2 - 7or14X<-3O B. *)-2orx 5C. x22 or x<5OD. x 814or X-3O
we will need to solve the first inequality,
5+x>=-3 , we will subtract -5 from both sides and the solution is
x>=-2
for the second inequality
6x+1<-29, we will subtract 1 from bothe sides and get
x<-5
is your choice B
Your brother is buying textbooks for college. He has to buy 3 math textbooks and 2 science textbooks. The total cost of his textbooks is $487. Write a linear equation to represent the cost of his textbooks.
Let's define the following variables,
x: cost of a math textbook
y: cost of a science textbook
He has to buy 3 math textbooks and 2 science textbooks, that is,
Total cost = 3x + 2y
The total cost of his textbooks is $487, then the linear equation is,
487 = 3x + 2y
Simplify the following expression.(12x-2.1)-(19x+6.9)
The given algebraic expression is
[tex](12x-2.1)-(19x+6.9)[/tex]To simplify this expression, we need to solve those parentheses in the first place, multiplying the sign in front of each of them.
[tex]12x-2.1-19x-6.9[/tex]Now, we reduce like terms. Remember that like terms are those who have the same variable, and those who don't have variables at all.
[tex]12x-19x-2.1-6.9=-7x-9[/tex]Therefore, the simplest form of the given expression is[tex]-7x-9[/tex]Following figure shows ABC with silencer the nearest 10th find AB in ABC
We have to find the length of AB.
We can use the Law of sines the tell us that the quotient between the sine of an angle and the length of the opposite side is constant for each of the three angles.
So we can write:
[tex]\begin{gathered} \frac{\sin(A)}{CB}=\frac{\sin(C)}{AB} \\ \frac{\sin(71\degree)}{6}=\frac{\sin(48\degree)}{AB} \\ AB=\frac{6\cdot\sin(48\degree)}{\sin(71\degree)} \\ AB\approx\frac{6\cdot0.743}{0.946} \\ AB\approx4.7 \end{gathered}[/tex]Answer: AB = 4.7
Which of the following shows the expansion of sum from n equals 0 to 4 of 2 minus 5 times n ?
(−18) + (−13) + (−8) + (−3) + 0
(−3) + (−8) + (−13) + (−18) + (−23)
2 + (−3) + (−8) + (−13) + (−18)
2 + 7 + 12 + 17 + 22
The option that indicates the required sum when n equals 0 to 4 of 2 minus 5 times n, is 2 + (−3) + (−8) + (−13) + (−18) (Option C)
What is the Sum of sequences?The sum of the terms of a sequence is called a series.
From the given sum of a sequence, we are to find the sum of the given sequence from n = 0 to n = 4
When n = 0
a(0) = 2 - 5(0)
a(0) = 2 - 0
a(0) = 2
When n = 1
a(1) = 2 - 5(1)
a(1) = 2 -5
a(1) = -3
When n = 2
a(2) = 2 - 5(2)
a(2) = 2 - 10
a(2) = -8
When n = 3
a(3) = 2 - 5(3)
a(3) = 2 - 15
a(3) = -13
When n = 4
a(4) = 2 - 5(4)
a(4) = 2 - 20
a(4) = -18
Hence the required sum is 2 + (−3) + (−8) + (−13) + (−18)
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The required sum is 2 + (−3) + (−8) + (−13) + (−18) when n equals 0 to 4 of 2 minus 5 times n, which is the correct answer that would be an option (C).
The given expression is (2 - 5n)
We to determine the sum of the given sequence from n = 0 to n = 4
Let the required sum is T₀ + T₁ + T₂ + T₃ + T₄
Substitute the value of n = 0 in the expression (2 - 5n) to get T₀
⇒ T₀ = 2 - 5(0) = 2 - 0 = 2
Substitute the value of n = 1 in the expression (2 - 5n) to get T₁
⇒ T₁ = 2 - 5(1) = 2 -5 = -3
Substitute the value of n = 2 in the expression (2 - 5n) to get T₂
⇒ T₂ = 2 - 5(2) = 2 - 10 = -8
Substitute the value of n = 3 in the expression (2 - 5n) to get T₃
⇒ T₃ = 2 - 5(3) = 2 - 15 = -13
Substitute the value of n = 4 in the expression (2 - 5n) to get T₄
⇒ T₄ = 2 - 5(4) = 2 - 20 = -18
Therefore, the required sum is 2 + (−3) + (−8) + (−13) + (−18)
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Solve the following addition and subtraction problems.3 km9hm9dam19 m+7km2 dam5sq km95 ha8,994sq m+11sq km11 ha9,010sq m44m−5dm72km47hm2dam−11 km55hm
As a well accepted rule to solve this problem, we would transform all values to the lower units.
so for the first question:
3 km 9hm 9 dam 19 m + 7 km 2 dam
3,000 m 900 m 90 m 19 m + 7,000 m 20 m
= 4,009 + 7,020
= 11,029 m
The second question:
5 sq.km 95 ha 8,994 sq.m + 11 sq.km 11 ha 9,010 sq.m
5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq 9,010 sq m
= 5,103,994 sq m + 11,119,010 sq m
= 16,223,004 sq m
The third question:
44 m - 5 dm
44 m - 0.5 dm
= 43.5 m
The fourth question:
72 km 47 hm 2 dam - 11 km 55 hm
72,000 m 4,700 m 20 m - 11,000 m 5,500 m
= 76,720 m - 16, 500 m
= 60,220 m
Please see photo checking my work I think it is all the students attending the college
Answer:
A population is the entire group that you want to draw conclusions about.
So, in this exercise, the population is all the students attending the college.
Johnathan works on IXL 5 nights per week. One week, he masters 7 skills. If he makes the sameamount of progress each night, how many skills does he master per night?Linear Equation:Solve:
In this problem
Divide total skills by the total night per week
so
7/5=1.4 skills per night
therefore
Let
x ----> number of night
y ----> total skills
so
y=(7/5)x ------> y=1.4xIn AUVW, VW = UV and mZU = 74º. Find mZV.
We will find the measure of angle V as follows:
*From theorem we have that angles that are opposite to congruent sides are congruent. So, Angle W will also have a measure o 74°. Now, we also have that the sum of all internal angles of a triangle add 180°, so the following is true:
[tex]U+V+W=180\Rightarrow74+V+74=180[/tex]Now, we solve for V:
[tex]\Rightarrow V=32[/tex]So, the measure of angle V is 32°.
Write 0.000000000054 in scientific notation
Answer:
5.4 × 10^-11
Step-by-step explanation:
Tina designed an electric skateboard that has a speed of 4 miles per hour. She wants to write a function that represents the distance the skateboard will travel over a given amount of time.Which is the dependent variable in this scenario?the skateboardthe speedthe time traveledthe distance traveled
ANSWER
The distance traveled
EXPLANATION
We want to identify the dependent variable from the scenario.
The dependent variable in a function is the variable that changes as a result of a change in the independent variable. This implies that it depends on the independent variable for its value.
From the scenario, the distance that the skateboard travels is dependent on the amount of time spent traveling.
Therefore, the dependent variable is the distance traveled.
how much of each ingredient would you need to make an identical recipe that serves 8 people explain your reasoning
LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice
The mass of a typical comet is about 1 x 10¹3 kg, while the mass of a typical asteroid is about 3 x 10¹⁹ kg.
Approximately how many times the mass of a typical comet is the mass of a typical asteroid?
100,000 times
300,000 times
1,000,000 times
O 3,000,000 times
The mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
It is given in the question that:-
Mass of a typical comet = [tex]1*10^{13}kg[/tex]
Mass of a typical asteroid = [tex]3*10^{19}kg[/tex]
We have to find the how many times the mass of a typical comet is the mass of a typical asteroid.
Mass of a typical asteroid/ Mass of a typical comet is given by:-
[tex]\frac{3*10^{19}}{1*10^{13}}=3*10^6[/tex]
We can write [tex]3*10^6[/tex] as 3,000,000.
Hence, the mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
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Use complete sentences to explain the process you would use to find the volume of the shipping box.(Trying to help my son with this)
Part A)
The given shipping box is a cuboid.
Recall that the longest length of the cuboid is diagonal.
The length of the longest item that fits inside the shipping box is the measure of the diagonal of the given box.
Given that measure breadth=16 inches and measure height = 12 inches.
Recall the formula for the diagonal d of the cuboid is
[tex]d=\sqrt[]{l^2+b^2+h^2}[/tex]We need to find the measure of the length of the cuboid.
Consider the base of the cuboid which is in rectangle shape.
Here breadth of the rectangle is 16 inches and diagonal of the rectangle is 24 inches.
Recall the formula for the diagonal of the rectangle is
[tex]diagonal_{}=\sqrt[]{l^2+b^2}[/tex]Substitute diagonal =24 inches and breath =16 inches, we get
[tex]24_{}=\sqrt[]{l^2+16^2}[/tex][tex]24_{}=\sqrt[]{l^2+256}[/tex]Taking square on both sides, we get
[tex]24^2_{}=l^2+256[/tex][tex]576-256=l^2[/tex][tex]320=l^2[/tex]Taking square root on both sides, we get
[tex]\sqrt[]{320}=l[/tex][tex]l=17.89\text{ inches}[/tex]Now, substitute l=17.89, b=16, and h=12 in the diagonal of the cuboid equation to find the diagonal of the cuboid.
[tex]d^{}=\sqrt[]{17.89^2+16^2+12^2}[/tex][tex]d^{}=\sqrt[]{320+256+144}=\sqrt[]{720}=26.83\text{ inches}[/tex]Hence the length of the longest item that fits inside the shipping box is 26.8 inches.
Part B)
Consider the length l=17.89 inches, b=16 inches, and height h=12 inches.
Recall the formula for the volume of the cuboid is
[tex]V=l\times w\times h[/tex]Substitute the length l=17.89 inches, b=16 inches, and height h=12 inches, we get
[tex]V=17.89\times16\times12[/tex][tex]V=3434.88inches^3[/tex]Hence the volume of the given shipping box is 3434.88 cubic inches.
Given the measure -845°, which answer choice correctly gives an angle measure coterminal with the given angle and on the interval,0 < 0 < 360
Given the measure -845° we can find its coterminal measure on the interval, [0,360) below
Explanation
For angles measured in degrees
[tex]\begin{gathered} β=α±360*k,where\text{ }k\text{ }is\text{ }a\text{ }positive\text{ }integer \\ -845°=\frac{-169}{36}π≈-4.694π \\ Coterminal\text{ }angle\text{ }in\text{ \lbrack}0,360°)range:\text{ 235\degree, located in the third quadrant.} \end{gathered}[/tex]Answer: Option A
The expression below is scientificnotation for what number?4.58x10^-2
Using the exponent rules, 10^-2 can be expressed as follows:
[tex]10^{-2}=\frac{1}{10^2}=\frac{1}{100}[/tex]Substituting into the expression in scientific notation, we get:
[tex]4.58\cdot10^{-2}=4.58\cdot\frac{1}{100}=\frac{4.58}{100}=0.0458[/tex]a box of cereal states that there are 75 calories in a 3/4 serving what is the unit rate for calories cup how many calories are there in 2 cups
We know that a box of cereal states that there are 75 calories in a 3/4 cup.
To find the unit rate for calories cup we must represent the the situation with an equation
[tex]\frac{75\text{ calories}}{\frac{3}{4}\text{ cup}}=\frac{x\text{ calories}}{1\text{ cup}}[/tex]Then, to find the unit rate for calories we need to solve the equation for x
[tex]x\text{ calories}=\frac{75\text{ calories}\cdot1\text{ cup}}{\frac{3}{4}\text{ cup}}=100\text{ calories}[/tex]Now, to find how many calories there are in 2 cups we must multiply the unit rate for calories by 2
[tex]x\text{ calories=100 calories}\cdot2=200\text{ calories}[/tex]Finally, the answers are:
- The unit rate for calories is 100 calories/cup.
- In 2 cups there are 200 calories.
I will send a picture of the problem and or question
The equivalency for grams to centigrams is:
1 gram = 100centigrams
To convert the units you can apply cross multiplication:
1gr_____100cgr
443gr____xcgr
[tex]\begin{gathered} \frac{100}{1}=\frac{x}{443} \\ x=443\cdot100=44300 \end{gathered}[/tex]This means that 443 grams equals to 44300 centigrams
*-*-*-*
The scale is done in a base of 10 and the grams are in its center with value 1.
To convert from smaller units to grater units you have to divide the given measurement by 10
And to convert from greater units to smaller units you have to multiply by 10.
For example if you have 1mg and want to convert it to grams you have to divide the value 3 times by 10, i.e. divide the value by 1000
[tex]\frac{1mg}{1000}=0.001g[/tex]If you want to convert 1 Kg into 1 decagram, multiply the value two times by 10, i.e. multiply it by 100
[tex]1\operatorname{kg}\cdot100=100\text{dag}[/tex]Write a quadratic function whose graph passes through (3,6) and has the vertex (-2,4) what is the value of Y
The representation of a quadratic eqauation in vertex form is
[tex]y=a(x-k)^2+h[/tex]The given vertex is,
[tex](k,h)=(-2,4)[/tex]And the given point through which the graph passes is,
[tex](x,y)=(3,6)[/tex]Substitute the values in the formula of quadratic equation.
[tex]\begin{gathered} 6=a(3-(-2))+4 \\ 6=a(3+2)+4 \\ 6=5a+4 \\ 5a=6-4 \\ 5a=2 \\ a=\frac{5}{2} \end{gathered}[/tex]Hence, the equation in vertex form will be,
[tex]\begin{gathered} y=\frac{5}{2}(x-(-2))+4 \\ y=\frac{5}{2}(x+2)+4 \end{gathered}[/tex]Based on your knowfedgs of the two data sets described below, would you espect a scatter plot describing the two data sets to have a positive, a negative, or nocorrelationduration of usage and the charge in the battery of a mobile phone
We expect the variable to have a negative correlation.
This means that the more we use the phone the lower the charge will be.
An old blackboard needs to be covered with cork. The picture shows the size of the blackboard. 40 in. 60 in. What is the area to be covered? A 100 in? B 200 in? C 1200 in 2 D2,400 in2
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
area = ?
Step 02:
A remodeling project calls for sanding a chair with a disksander. The sanding disk used on the sander has a radiusof 4.5 Inches. Find the area of the disk. Use 3.14 for
Keeshonbought Packages of pens represented by P there were four pence in each package Keyshawn gave six to his friends which expression shows this situation
The expression that shows when Keeshon bought Packages of pens represented by P is 24p.
What is an expression?An expression is used to illustrate the information that's given regarding a data.
Let the pens be represented by p.
In this case, there there were four pend in each package and Keyshawn gave six to his friends. This will be:
= 6(4 × p)
= 6(4p)
= 24p
This shows the expression.
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In a class of 6, there are 4 students who are secretly robots. If the teacher chooses 2 students, what is the probability that neither of them are secretly robots?i know how to get 2/6 but how do i get the other fraction?
The chance of the first student chosen not secretly being a robot is 2/6, but if the student is secretly a robot, then it doesn’t matter who the second student chosen is, because “neither” cannot be obtained.
So, 2/6th the time we care about the second student. There is in this case 1 non robot among the 5 remaining students, so the chance is 1/5 of picking that second non robot.
Hence;
2/6 x 1/5 = 2/30 = 1/15
