It took Valerie 80 minutes to drive 120 miles. Which of the following unit rates expresses how fast Valerie was traveling?
60 miles per hour 70 miles per hour
80 miles per hour 90 miles per hour
Answer:
90 miles per hour
Step-by-step explanation:
Divide distance by time to get speed.
\(\frac{120}{80}\)=1.5 miles per minute
60 minutes in an hour
1.5(60)=90 miles an hour
Thank for doing it love you
Answer:
1 is 1/9 2 is 1/9 3 is 5/9 4 is 8/9
Step-by-step explanation:
A(Ab AC AA) B(ba bb bc) C(ac bc cc)
The system shown below is :
x + 3y =4
3x + 9y = 12
Answer
this look at the screenshop
Which of the following represents the parameterization of a circle of radius r in the xy-plane, centered at (a,b), and traversed once in a clockwise fashion
The parameterization of a circle of radius r in the xy-plane, centered at (a, b), and traversed once in a clockwise fashion can be represented by the following equations:
\(\[ x = a + r \cos(t) \]\[ y = b - r \sin(t) \]\)
where:
- (a, b) represents the center of the circle,
- r represents the radius of the circle,
- t represents the parameter that ranges from 0 to 2π (or 0 to 360 degrees) to traverse the circle once in a clockwise fashion.
In the equation for x, the cosine function is used to determine the x-coordinate of points on the circle based on the angle t. Adding the center's x-coordinate, a, gives the correct position of the points on the circle in the x-axis.
In the equation for y, the sine function is used to determine the y-coordinate of points on the circle based on the angle t. Subtracting the center's y-coordinate, b, ensures that the points are correctly positioned on the y-axis.
Together, these equations form a parameterization that represents a circle of radius r, centered at (a, b), and traversed once in a clockwise fashion.
Learn more about parameterization: https://brainly.com/question/33611063
#SPJ11
True or False. When conducting a cluster sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous.
False. When conducting a cluster sample, it is typically preferable to have more heterogeneous clusters with fewer individuals.
Why is this statement false?This is due to the fact that when clusters are diverse, it is crucial to appropriately represent the population by capturing its diversity.
In such situations, the danger of sampling bias is increased by having fewer clusters with more individuals because a larger number of people from a single heterogeneous cluster would not fairly represent the overall community. Incorrect estimates and conclusions may result from this.
Having fewer clusters with more individuals, on the other hand, can assist raise the precision of the estimates when clusters are homogeneous by lowering the variance associated with sampling from a single cluster. In general, to achieve a precise representation of the population and to lessen the chance of sampling bias, the number of clusters and the size of each cluster should be balanced.
Learn more about heterogeneous clusters here:
brainly.com/question/24013238
#SPJ4
y=586x=1000 1172x+2y=2000
Answer:
klmqe
Step-by-step explanation:
Answer:
The answer is that this equation is false it does not equal. 688792≠2000
Step-by-step explanation:
If yu plug in the values of x and y you will get 688792 and that is not equal to 2000.
What is the slope of (-3, -2) and (-1, -5) ??
Answer:
-3/2 or -1 1/2
Step-by-step explanation:
The slope, plugging into the equation (y_2-y_1)/(x_2-x_1) would be -5 + 2 / -1 + 3, or -3/2, which can also be - 1 1/2
Answer:
-3/2
Step-by-step explanation:
slope ('m') formula: (difference of the y-values) ÷ (difference of the x-values)
m = -2-(-5) ÷ -3-(-1)
m = 3 ÷ -2
slope = -3/2
The freight elevator of a building can safely carry a load of at most 4000 lb. A worker needs to move supplies in 50-lb boxes from the loading dock to the fourth floor of the building. The worker weighs 160 lb. The cart he uses weighs 95 lb.
(A) Write and solve an inequality to determine the greatest number of boxes he can move in one trip.
(B) The worker must deliver 310 boxes to the fourth floor. How many trips must she make?
The inequality that represents the greatest number of boxes he can move in one trip is 255 + 50b ≤ 4000.
The solution of the inequality is 74.
The number of trips he would make to deliver 310 boxes is 5.
What is the solution of the inequality?Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≤
The form of the inequality is:
Weight of the worker + weight of the cart + (weight of the boxes x number of boxes) ≤ 4000
160 + 95 + (50 x b) ≤ 4000
255 + 50b ≤ 4000
In order to determine the value of b, take the following steps:
Combine similar terms:
50b ≤ 4000 - 255
50b ≤ 3745
b ≤ 3745 / 50
b ≤ 74.9
The number of boxes he can carry is 74
Number of trips = total number of boxes / number of boxes he can carry in one trip
= 310 / 74
= 4.1
= 5 trips
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
Solve questions 7,8, and 9 pls, the first person to solve I will name brainliest.
1) Note that the condition that proves that a quadrilateral is a parallelogram are:
2) The statements from the above list that are specific to a Rhombus are:
Sides are all congruentBoth pairs opposite angles are congruentDiagonals are perpendicularDiagonals bisect each other.3) The figures below that are parallograms are:
Option A
Option B; and
Option D.
A parallelogram is a type of quadrilateral with some special properties. Here are all the qualities of a parallelogram:
Opposite sides are congruent: This means that the two pairs of opposite sides have the same length.
Opposite sides are parallel: This means that the two pairs of opposite sides are always parallel to each other.
Opposite angles are congruent: This means that the two pairs of opposite angles have the same measure.
Consecutive angles are supplementary: This means that any two angles that are adjacent or consecutive to each other add up to 180 degrees.
Diagonals bisect each other: This means that the two diagonals of a parallelogram intersect at their midpoint, and each diagonal divides the parallelogram into two congruent triangles.
Diagonals are not congruent: This means that the two diagonals of a parallelogram have different lengths.
Learn more about Rhombus:
https://brainly.com/question/27870968
#SPJ1
PART G: Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?
Part H
Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.
Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.
Part J
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given two angles and the side between them.
Under Sides, enter 5 for a. Under Angles, enter 30 for B and 50 for C. Then click Calculate. How many triangles can be created from the given conditions?
Part K
Return to the Calculator tab, and click the Clear button to begin a new calculation. This time, you’ll check for valid triangles given three sides of specified length.
Under Sides, enter 6 for a, 7 for b, and 13 for c. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given side lengths.
please help!
The solutions are given below.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Part A
the dotted line formes the thrid side of the triangle.
part B
The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.
part c
If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.
part D
You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.
part e
The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.
part f
Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters
To learn more on triangle click:
brainly.com/question/29126067
#SPJ1
32.8+3.27−0.15
..............................
Answer:
32,8+3,27=36,07
36,07-0,15=35.92
Step-by-step explanation:
what is a indirect proportion?
Answer:
Indirect or inverse proportion is a relation between two quantities where an increase in one leads to a decrease in the other, and vice-versa. It is just the opposite of direct proportion.
Step-by-step explanation:
pls help if you can asap!!!!
Answer: x= 6
Step-by-step explanation:
Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.
You can see they do not look the same so they add up to equal 180
12x + 3 +105 = 180
12x + 108 = 180
12x = 72
x = 6
$2,000 is invested in an account earning 5.4% interest (APR), compounded
continuously. Write a function showing the value of the account after t years,
where the annual growth rate can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine
the percentage of growth per year (APY), to the nearest hundredth of a
percent.
A function showing the value of the account after t years,
⇒ \(A = 2000(1 + 0.054)^{t}\)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
$2,000 is invested in an account earning 5.4% interest (APR).
Now, For interest compounding continuously, we need this formula:
⇒ \(A = P(1 + \frac{r}{n} )^{nt}\)
Where, A is Amount at some time t
P is the initial amount
r is the interest rate (as a decimal)
t is number of years
For our problem, we would plug in:
P = 2,000
r = 0.054
Hence, We get;
A function showing the value of the account after t years,
⇒ \(A = 2000(1 + 0.054)^{t}\)
For one year the interest would be like this;
⇒ (1 + 0.054) - 1
⇒ 0.054
⇒ 5.4%
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
The ratio of girls to boys at a party is 5:4. if there are 20 girls in the class, how many boys are there.
Answer:
16 boys
==========================
Let the number of boys be b and girls be g.
The ratio is:
g/b = 5/4And the number of girls is:
g = 20Substitute the number into ratio and find the value of b:
20/b = 5/4b = 20*4/5b = 16consider the following code snippet: vector vect data(90); vect data.pop_back; what is the size of the vector vectdata after the given code snippet is executed? group of answer choices 89 2 88 90
The vector vectdata will retain its original size of 90, and none of the provided answer choices (89, 2, 88, 90) are correct.
The code snippet you provided has a syntax error. The correct syntax to call the pop_back function on a vector is vectdata.pop_back(), with parentheses at the end. However, in the given code, the parentheses are missing, causing a compilation error.
Assuming we fix the syntax error and call the pop_back() function correctly, the size of the vector vectdata would be reduced by one. The pop_back() function removes the last element from the vector. Since the vector was initially created with a size of 90 using vector vectdata(90), calling pop_back() will remove one element, resulting in a new size of 89.
However, in the given code snippet, the missing parentheses make the line vectdata. pop_back an invalid expression, preventing the code from compiling successfully. Therefore, the vector vectdata will retain its original size of 90, and none of the provided answer choices (89, 2, 88, 90) are correct.
To know more about expression refer to
https://brainly.com/question/14083225
#SPJ11
what’s the answer ??
Answer:
Left box: 1/2n
Right box = 2n - 22
Step-by-step explanation:
Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.
Thus, you want to put 1/2n in box on the left.
Twice the number and 22 less than this is given by: y: 2n - 22 less than this means we subtract. Thus, we have 2n - 22 as the numerator on the right hand side of the equation.
Thus, you want to put 2n - 22 in the box on the right.
Please help me I I will give you a Brainly
Step-by-step explanation:
by deleting
9y = -9
y = -1
6x - 4 = -10
6x = -6 then x = -1
It costs $363 to make 90 bags of cotton candy and $440 to make 200 bags of cotton candy.
a) find the cost equation.
Answer:
363=90bags
then you look into it and say
440=200bags
Find the measure of angle BAC.
Answer:
\(\angle 72=BC-86/2\)
\(144+86=BC\)
\(BC=230\)
\(BC=230/2\)
\(\angle BAC= 115\)°
~OAmalOHopeO
\(\huge\boxed{Write\;equations\;for\;the\;following...}\\\\1...\;\;(0, -2) & (3,0)\\2...\;\;(0, -3) & (-4, -5)\\3...\;\;(-3,-4) & (4,3)\\\\\\\boxed{Please\;show\;work!}\)
Answer:
1. y = -2/3x + 2
2. y = 2/4x + -3
3. y = 1x -1
Answer: see below
Step-by-step explanation:
Step 1: Find the slope (m) using the formula: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)
Step 2: Plug in the slope (m) and one of the points (x₁, y₁) into the Point-Slope formula. y - y₁ = m(x - x₁)
1. (0, -2) and (3, 0)
Step 1: \(m=\dfrac{-2-0}{0-3}\quad =\dfrac{-2}{-3}\quad =\dfrac{2}{3}\)
Step 2: \(y-0=\dfrac{2}{3}(x-3)\)
\(y=\dfrac{2}{3}(x-3)\)
\(\large\boxed{y=\dfrac{2}{3}x-2}\)
2. (0, -3) and (-4, -5)
Step 1: \(m=\dfrac{-3-(-5)}{0-(-4)}\quad =\dfrac{-3+5}{0+4}\quad =\dfrac{2}{4}\quad =\dfrac{1}{2}\)
Step 2: \(y-(-3)=\dfrac{1}{2}(x-0)\)
\(y+3=\dfrac{1}{2}x\)
\(\large\boxed{y=\dfrac{1}{2}x-3}\)
3. (0, -3) and (-4, -5)
Step 1: \(m=\dfrac{-4-3}{-3-4}\quad =\dfrac{-7}{-7}\quad =1\)
Step 2: \(y-3=1}(x-4)\)
\(y-3=x-4\)
\(\large\boxed{y=x-1}\)
Write the following linear function in slope intercept form.
a^-m=
(a) 1/a^m (b) 1/a^-m (c) a/m (d) 1/am
The reciprocal of \(A^m\) is \(1/A^m.\)
This means that\(A^{-m\) is equivalent to\(1/A^m.\)
The correct answer is\((a) 1/a^m.\)
To understand why, let's break down the expression \(A^{-m}.\)
In mathematics, a negative exponent indicates the reciprocal or inverse of the base raised to the positive exponent.
In this case, \(A^{-m\) can be rewritten as \(1/A^m.\)
The reciprocal of a number is obtained by flipping the fraction or raising it to the power of -1.
So,\(1/A^m\) means the reciprocal of\(A^m.\)
To further simplify, we can rewrite \(A^m\) as \((A^m)^1,\) using the property of raising a power to another power.
Now, by applying the power of a product rule, we have \(A^{(m \times 1)},\) which simplifies to\(A^m\).
Therefore, the reciprocal of \(A^m\) is \(1/A^m\).
This means that \(A^{-m }\) is equivalent to \(1/A^m.\)
The correct answer is (a) \(1/a^m.\)
In summary, the correct answer is (a)\(1/a^m\)for \(A^{-m}.\)
For similar question on expression.
https://brainly.com/question/1859113
#SPJ8
CARPENTRY A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood. The rectangle must be
sawed along the dashed line in the figure.
The measure of angle1 in the given rectangular figure is 64° .
In the question ,
it is given that ,
the one of the angle is 116° .
From the figure below ,
we can see that
the dashed line is a transversal to AB and CD ,
the angles on the line AB form a linear pair ,
So , angle2 + 116° = 180°
angle2 = 180° - 116°
angle2 = 64°
Since the side panel of the podium is cut from rectangular piece
the figure is representing two parallel lines , cut by the transversal .
By the property of transversal that alternate interior angles are equal in measure ,
angle 1 = angle 2
hence , angle 1 = 64° .
Therefore , The measure of angle1 in the given rectangular figure is 64° .
Learn more about Transversal here
https://brainly.com/question/9610896
#SPJ1
If the temperature outside increases by 3 1/2 degrees every 1 1/2 hours, by how much will the temperature increase after 4 hours?
please answer in fractions.
Part 1:
What is the rate per hour of the temperature increase?
Part 2:
How much will the temperature increase after 4 hours?
Answer:
Part 1: 7/3 degrees/hour
Part 2: 28/3 degrees
Step-by-step explanation:
Part 1:
3 1/2 degrees per 1 1/2 hours =
= (3 1/2)/(1 1/2)
= (7/2) / (3/2)
= 7/2 * 2/3
= 7/3 degrees/hour
The rate is 7/3 degree per hour
Part 2:
In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.
4 hours * 7/3 degree/hour = 28/3 degrees
In a fruit cocktail for every 100ml Orange juice you need 12ml Apple juice and 8ml of coconut milk what is the ratio of Apple juice to coconut milk to orange juice expressed in its simplest form
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 78% of the carbon-14 expected in living matter, when did the tree die?
Answer:
2,700 years
Explanation:
We were given the following details:
Half-life of carbon-14, T = 5600 years
78% of carbon-14 is left. This indicates that the amount of carbon-14 left is 78% of the initial amount:
\(0.78\times A_0\)We will calculate the time since when the tree died as shown below:
\(\begin{gathered} 0.78\times A_0=A_0\times(0.5)^{\frac{t}{T}} \\ T=5600years \\ t=? \\ \text{Substitute the variables into the formula, we have:} \\ 0.78=(0.5)^{\frac{t}{5600}} \\ \text{Take the natural logarithm of both sides, we have:} \\ ln(0.78)=\frac{t}{5600}\times ln(0.5) \\ \text{Make ''t'' the subject of the formula, we have:} \\ t=5600\times\frac{ln(0.78)}{ln(0.5)} \\ t=5600\times0.35845397091 \\ t=2007.34223711\approx2007 \\ t=2,007years \end{gathered}\)Therefore, the tree died 2,700 years ago
Find the vertex and focus of the
parabola.
x2 + 6x – 8y + 1 = 0
Answer:
Step-by-step explanation:
Vertex: -3, -1
Focus: -3, 1
Vertex of the parabola is (-3,-1)
Focus is (-3,1)
What is the vertex form of parabola?The standard form of the parabola is given by y = ax2 + bx + cThe vertex form of the parabola is y-k = a(x - h)^2vertex of the parabola is (h,k)Focus of the parabola is (h,k+p)Given parabola equation is x^2+6x-8y+1=0
x^2+6x = 8y-1
x^2+6x+9 = 8y-1+9
(x+3)^2 = 8y+8
(x+3)^2 = 8(y+1)
(y+1) = 1/8 (x+3)^2
Here vertex V(h,k) = (-3,-1)
Focus = (-3,1)
Hence, Vertex of the parabola is (-3,-1)
Focus of the parabola is(-3,1)
Learn more about parabola here:
https://brainly.com/question/4291574
#SPJ2
The following table shows how much Dave gave each of his kids for allowance last month Find the median allowance
Answer:
7
Step-by-step explanation:
1. arrange the numbers from smallest to biggest
2. cross on each side until you reach a middle number
3. if there's two digits , add them both and divide by two
Answer:
7
Step-by-step explanation:
How many arrangements of letters in REPETITION are there with the first E occurring before the first T?
The number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560
To find the number of arrangements of letters in the word REPETITION where the first E occurs before the first T, we can approach the problem by breaking it down into simpler steps.
Step 1: We need to determine the total number of arrangements of the letters in REPETITION. Since there are 9 letters in the word, the total number of arrangements can be calculated using the formula for permutations of n objects taken r at a time, which is n!/(n-r)!. In this case, we have n=9 and r=9, so the total number of arrangements is 9! = 362,880.
Step 2: We need to count the number of arrangements where the first E occurs before the first T. To do this, we can first fix the positions of the first E and T in the word. There are 9 possible positions for the first letter, 8 remaining positions for the second letter, and so on, down to 1 possible position for the ninth letter. This gives us a total of 9x8x7x6x5x4x3x2x1 = 362,880 possible arrangements of the letters in REPETITION.
However, we want to exclude the arrangements where the first T appears before the first E. To do this, we can fix the position of the first T and count the number of arrangements of the remaining letters. There are 8 possible positions for the first T, and then 7 remaining positions for the second letter, and so on, down to 1 possible position for the eighth letter. This gives us a total of 8x7x6x5x4x3x2x1 = 40,320 arrangements where the first T appears before the first E.
Therefore, the number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560.
Learn more about REPETITION here:
https://brainly.com/question/28084537
#SPJ11