Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.
As given in the question,
Given equation :
|x – 55| = 4.2
To determine the maximum and minimum speed in miles per hour from the given equation we have,
x-55 = 4.2 or x-55 =-4.2
Add 55 both the side of the equation,
x-55 +55 =4.2+55 or x-55+55 = -4.2 +55
x =59.2 or x = 50.8
Maximum speed is 59.2 determine by equation x-55 = 4.2
Minimum speed is 50.8 determine by equation x-55 = -4.2
Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to
x -55 =4.2.
The complete question is:
On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?
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professor horvat designs a study to assess the work satisfaction and home-life satisfaction of a group of graduate students. she administers the same measures of work and home-life satisfaction on two occasions, 1 year apart. she finds at both the first time point and the second time point there is a strong correlation between work satisfaction and home-life satisfaction. which type of correlations are these?
The type of correlation founded in the study by assessing the work and home life satisfaction measure identically at two occasions, a year apart, is a cross-sectional correlation.
Cross-sectional correlation is a non-experimental research design that uses data collected from a single time point. It is used to generate a static portrait of research variables. As opposed to serial correlation which is a correlation of one variable at different times, cross- sectional correlation is a correlation of two variables at the same time.
In the given study, professor measured the work satisfaction and home-life satisfaction at one time point and repeated it after a year at the second time point. She found a strong correlation between variable at both time points. Hence, it is cross-sectional correlation.
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A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?
Answer:
8 seconds
Step-by-step explanation:
See attach worksheet.
what is 1/3 of 9 cookies and lollipops
∵ 1/3 of 9 means multiply it by 9
[tex]\begin{gathered} \because\frac{1}{3}\times9=\frac{1\times9}{3}=\frac{9}{3} \\ \therefore\frac{1}{3}\times9=3 \end{gathered}[/tex]3 is 1/3 of 9 cookies and lollipops
Answer:
1/3 of 9 is 3.
Step-by-step explanation:
Think of it like this: what number can be added to itself 3 times to get 9? The answer is 3! 3 + 3 + 3 = 9. So, 1/3 of nine is 3 because 9 split into 3 sections would be 1/3 + 1/3 + 1/3 = 1 and 3 + 3 + 3 = 9. So, 1/9 simplified is 1/3!
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Find the value of X using your method
Answer:
[tex]x = 30[/tex]
Step-by-step explanation:
In the diagram above, MN is a straight line which equals 180.
RL is vertically opposite to KS
(Vertically opposite angles are equal ⟹RL = KS).
So, MN becomes:
[tex]90 + 2x + 30 = 180[/tex]
Collect like terms
[tex]90 + 30 + 2x = 180→120 + 2x = 180→2x = 180 - 120→2x = 60[/tex]
Divide 2x = 60 by 2
[tex]x = \frac{60}{2} [/tex]
Therefore: [tex]x = 30[/tex]
It took Brian 3 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 23 mph and make the return drive in only 2 hours. Find his average speed on the return drive.The equation from part 2 is 3x=2(x+23)Step 3 of 3: Solve the equation found in part 2 for x. Use this information to answer the given word problem.
Answer:
69 mph
Explanation:
The equation that represents this situation is:
[tex]3x=2(x+23)[/tex]We are required to determine Brian's average speed on the return drive.
To do this, we first find the value of x.
[tex]\begin{gathered} \text{Open the bracket} \\ 3x=2x+46 \\ \text{Subtract 2x from both sides} \\ 3x-2x=46 \\ x=46\; \text{mph} \end{gathered}[/tex]Using the value of x, we find the average speed on the return drive.
[tex]x+23=46+23=69\text{mph}[/tex]Therefore, the average speed on the return drive will be 69 mph.
In the figure below, AX'Y'Z' is a dilation of AXYZ. Find the scale factor of the dilation, andspirit as an enlargement or a reduction. What is the scale factor?What is the Classify?
The scale factor can be obtained by determining the ratio of the length of the sides of the old and new figures.
In other words, it can be obtained by stating that:
[tex]\text{scale factor=}\frac{lengthofsideoftriangleX^IY^IZ^I}{\text{length of side of triangle XYZ}}\text{ }[/tex]Specifically, we can say that:
[tex]\text{scale factor=}\frac{X^IY^1}{XY}=\frac{X^IZ^I}{XZ}=\frac{Y^IZ^I}{YZ}[/tex]Now, if each block (or cell) on the graph represents 1 units, we have that:
X'Y' = 10 units and XY = 5 units
Therefore:
[tex]undefined[/tex]can you please answer work the math problem the easiest quick way please
Given: the three points are plotted on graph.
For the first point it is observed that,
For the x =3/2 the value is y=6/2
For second point ,
For x= 9/2 the y value is y=12/2
For the third point ,
For x= 15/2 the y value is y=18/2
According to obtained information it matched to option J)
Answer: Option J)
select all the angles that are congruent to <6
The angles that are congruent to angle 6 in the given diagram are:
∠2, ∠3, and ∠5.
What are Congruent Angles?Interior angles that lie opposite to each other along a transversal that cut across the parallel lines they are found on are said to be congruent angles based on the alternate interior angles theorem.
Also, vertical angles have angle measure that are the same, that is, they are congruent as well, so also are corresponding angles.
In the image given, angles 3 and 6 are alternate interior angles. Therefore, they are congruent.
∠5 is congruent to ∠6 because they are vertical angles.
∠2 is congruent to ∠6 because they are corresponding angles.
The angles that are congruent to angle 6 are: angles 3, 5, and 2.
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I need help understanding, how do I solve this?
3 – [–(–1)]
Answer:
3-[1]
3-1
2
Step-by-step explanation:
=//7777/))_+++++++4
In triangle ABC measure of angle A equals 45°. The altitude divides the side AB into two parts of 20 and 21 units. Find BC.
In triangle ABC, BC = 29 units.
Given,
In Δ ABC, ∠A = 45°.
A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.
Let altitude meet AB on D.
So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°
In ΔADC,
tan A = DC/AD
tan 45° = DC/20
1 = DC/20
DC = 20 units
In ΔBDC,
BC² = BD² + DC² (Pythagorean Theorem)
= 21² + 20²
= 441 + 400
= 841
BC = √841
= 29
Hence, BC = 29 units.
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16 more than s is at most -80 interval notation
The answer in interval notation is given by {96, ∞}.
What is an interval notation?An interval notation can be defined as a set of real numbers which comprises all of the real numbers that are representing a continuous function and lies between two set of numbers.
This ultimately implies that, an interval notation can be used as a technique for writing all of the subsets of the real number line.
Translating the given word problem into an inequality algebraic expression:
16 - s ≤ -80
Adding 80 to both sides of the expression, we have:
80 + 16 - s ≤ -80 + 80
96 - s ≤ 0
Rearranging the expression, we have:
s ≥ 96
Therefore, we have {96, ∞}.
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Complete Question:
Translate and solve: 16 more than s is at most -80.
Give your answer in interval notation.
I NEED HELP WITH THIS ASAP!!!! The following diagram describes the mixture's volume of blue and red paint. What is the ratio of blue color to real paint in the mixture?
The ratio of blue color to red paint in the mixture is 5 :3.
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of one value compared to the frequency of another value. The sign that is used to measure ratio is :.
In order to determine the ratio, count the number of blue tiles and the number of red tiles.
Number of blue tiles = 10
Number of red tiles = 6
The ratio of blue to red is 10 : 6. When expressed in its simplest form, it is 5 : 3.
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Use inductive reasoning to find a pattern and then make a reasonable conjecture for the next number in the sequence.
We will find the pattern as follows:
105 - 104 = 1
104 - 102 = 2
102 - 99 = 3
99 - 95 = 4
95 - 90 = 5
90 - 84 = 6
So, it is reasonable to assume that the next value will be 77.
-3a - 10 = 20
Solve the following equation
Answer:
a = -10
Step-by-step explanation:
-3a - 10 = 20
add 10 to both sides:
-3a - 10 + 10 = 20 + 10
-3a = 30
divide both sides by -3:
-3a/-3 = 30/-3
a = -10
Answer:
a=- 10
Step-by-step explanation:
-3a - 10 = 20
+10=+10
you end up with -3a=30
divide by -3 both side
a=-10
GEOMETRY
Circle the one contradictory piece of information in each of the following sets of information
Answer:
Step-by-step explanation:
Item 1
<RSL is not ≅ < XYM
Item 2
< LST and < QRX are not supplementary (they are congruent)
Item 3
m < LST = 120 - there is no evidence for this.
Item 4
< JRS = <LST
so, If < LST = 120, then this can't be 195
Find the median and mean of the data set below:
20, 46, 20, 26
what is the slope for 5/3 x-4
Answer:
The slope is 5/3
Step-by-step explanation:
y = 5/3x - 4
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 5/3 and the y intercept is -4
33% of millennials rely on blogs before making a purchase and eight
out of 10 millennials never buy anything without reading a review first.In a sample size of 75 Millennials, how many people use blogs to make a purchase?In a sample size of 75 Millennials, how many people never buy anything without reading a
review first?
24 millennials will use blogs to make a purchase and 60 millennials will never buy anything without reading a review first.
Here, we are given that 33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first.
a. If there is a sample of 75 Millennials, out of these 33% will use blogs to make a purchase.
Thus,
33% of 75
= 33/100 × 75
= 33/4 × 3
= 99/4
= 24.75
Since, the number of millennials cannot be a decimal number, we approximate it to the lowest integer, that is, 24.
Thus, 24 millennials will use blogs to make a purchase.
b. Now, if there is a sample of 75 Millennials, out of these 8 out of 10 will never buy anything without reading a review first.
8 out of 10 in percentage terms will be-
8/10 × 100
= 80%
Thus,
80% of 75
= 80/100 × 75
= 80/4 × 3
= 20 × 3
= 60
Thus, 60 millennials will never buy anything without reading a
review first.
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Find the possible outcomes for each event in rolling a number die. Then find the probability of each event as a fraction, decimal and percent.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating probability
[tex]P(event)=\frac{number\text{ of favorable outcomes}}{number\text{ of possible outcomes}}[/tex]STEP 2: State the number of possible outcomes
[tex]\begin{gathered} A\text{ die has 6 faces numbered 1,2,3,4,5,6} \\ Therefore,\text{ the number of possible outcomes will be 6} \end{gathered}[/tex]STEP 3: Answer question A
Rolling a number less than 7
[tex]\begin{gathered} Numbers\text{ less than 7}\Rightarrow6,5,4,3,2,1 \\ n(numbers\text{ less than 7\rparen}\Rightarrow6 \\ \\ By\text{ substituting the values into the formula in step 1,} \\ P(Rolling\text{ a number less than 7\rparen}\Rightarrow\frac{6}{6}=1 \\ \\ Percentage\Rightarrow\frac{1}{1}\times100=100\% \end{gathered}[/tex]Hence,
Possible outcomes are 6,5,4,3,2,1
Probability = 1
Probability = 1.0 as decimal
Probability = 100% as percentage
STEP 4: Answer Question B
Rolling an 8
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow8 \\ n(8)\Rightarrow0 \\ Probability=\frac{0}{8}=0 \\ Percentage=0\times100\%=0\% \end{gathered}[/tex]Hence,
Possible outcome is 0 since there is no face of the die having 8
Probability = 0
Probability = 0.0 as decimal
Probability = 0% as percentage
STEP 5: Answer Question C
Rolling a number greater than 4
[tex]\begin{gathered} Possible\text{ Outcomes}\Rightarrow5,6 \\ n(Possible\text{ outcomes\rparen}\Rightarrow2 \\ Probability=\frac{2}{6}=\frac{1}{3}\approx0.333 \\ Percentage=\frac{1}{3}\times100=\frac{100}{3}=33.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 5,6
Probability = 1/3
Probability = 0.333 as decimal
Probability = 33.33% as percentage
STEP 6: Answer Question D
Rolling a number other than 6
[tex]\begin{gathered} Possible\text{ outcomes}\Rightarrow1,2,3,4,5 \\ n(Possible\text{ outcomes\rparen}\Rightarrow5 \\ Probability=\frac{5}{6}=0.8333 \\ Percentage=\frac{5}{6}\times100=83.33\% \end{gathered}[/tex]Hence,
Possible outcomes are 1,2,3,4,5
Probability = 5/6
Probability = 0.8333 as decimal
Probability = 83.33% as percentage
Write the equation of the line passing through the points (-7.4) and (7.2).
The equation of the line is
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answer: y = -1/7x + 3
Step-by-step explanation:
Write the equation of the line passing through the points (-7.4) and (7.2).
First, find the slope of the two points by the y2-y1/x2-x1 slope formula.
The slope is -1/7.
Then, use the point slope form y-y1 = m(x-x1).
Question Progress
Homework Progress
7/21 Marks
Solve the equation
3x-2
4
-
2x-5
3
=
1+x
6
Answer: x= 1.20833
The way it was written was a little confusing but hope this helps, This may be wrong just re write it for me and it should be correct next time.
Step-by-step explanation:
Step 1: Make parentheses
( 3x - 2 ) 4 ( -2x - 5 ) 3 = ( 1 + x ) 6
Step 2: Solve parentheses ( Multiplication and division first )
(4 * 3x = 12x) - (4 * 2 = 8) -> 12x - 8
(-2x * 3 = -6x) - (3 * 5 = 15) -> -6x - 15
(6 * 1 = 6) + (6 * x = 6x) -> 6 + 6x
New and improved equation:
-12x - 8 - 6x - 15 = 6 + 6x
Step 3: add like terms
-12x - 6x = -18x
-8 - 15 = -23 so...
-18x - 23 = 6 + 6x
Step 4: solve it
-18x - 23 = 6 + 6x
+ 23
-18x = 29 + 6x
-6x
-24x = 29
x= 1.20833
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by what factor does the intensity increase for each whole number increase in the richter scale?
Answer:
By adding the gravity of the earth ang subtracting the number of the enumeration and multiply the square root of need to be the first divorcee you know that I love ckicen nuggets
Step-by-step explanation:
Me to mama o sige na kain na kau
Carter wants to use the model above to solve 273 ÷ 13. Explain how he would find parts A, B, and C of the model. Unfortunately I can’t show the model because “it hurts their feelings”
Answer: The answer to the division problem is 21
Answer: I know 273 divided by 13 is 21 but without the model I don't know what else you need. sorry!
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
If function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
The function is
f(x) = [tex]x^2[/tex] + 4x -1
The function is the expression that represents the relationship between one variable and another variable. If one variable is dependent variable then the another variable is independent variable.
The value of g(x) = f(x+4)
First we have to find the value of f(x+4)
Substitute the values in the function
f(x) = [tex]x^2[/tex] + 4x -1
f(x+4) = [tex](x+4)^2[/tex] + 4(x+4) - 1
= [tex]x^2[/tex] + 8x +16 + 4x+16 - 1
Rearrange the terms and combine the like terms
= [tex]x^2[/tex] + 8x+4x + 16+16-1
= [tex]x^2[/tex] + 12x +31
Hence, if function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
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Josie sold 790 tickets to a local car show for a total of $4,390.00. A ticket for a Child costs $4.00 and adult ticket costs $7.00. How many of each ticket did she sell? A) Children’s ticket? B) Adult Ticket?
Let's define the following variables first.
A = number of tickets sold for adults
C = number of tickets sold for children
From the question, we can say that or form the following equations:
1. A + C = 790 tickets
2. $7A + $4C = $4, 390
The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.
[tex]7(790-C)+4c=4,390[/tex]From that, we can solve "C" by solving the equation formed above.
[tex]\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}[/tex]Therefore, 380 tickets for children were sold.
Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.
[tex]\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}[/tex]The perimeter of a rectangular garden is 252 feet. If the width of the garden is 53 feet , what is its length
The perimeter of a rectangle is given by:
[tex]P=2l+2w[/tex]Where:
P = perimeter = 252 ft
w = width = 5 ft
l = lenght
Then, substitute the values:
[tex]252=2l+2(53)[/tex]And solve for l:
[tex]\begin{gathered} 252=2l+106 \\ 252-106=2l+106-106 \\ 146=2l \\ \frac{146}{2}=\frac{2l}{2} \\ l=73 \end{gathered}[/tex]Answer: length = 73 ft
a=3,k=12,z=6,h=4 Evaluate algebraic expression
k-a+h
Answer:
[tex]k - a + h[/tex]
Step-by-step explanation:
Hope this helps you! :))
Jason compares the price of x pizzas which all have a one-time delivery fee. This question has two parts.
18.30x +3.75
19.35x + 5.00
13.25x +3.99
What is the cheapest pizza without a delivery fee?
What is the cheapest delivery fee?
The cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.
What is the cheapest delivery fee?Delivery fees are used to defray the cost of transporting food to customers. We'll discuss the various ways that restaurants might approach this revenue channel and how these fees are calculated based on how a restaurant runs its delivery service.A price assessed by the delivery business as compensation for the service.
Taxes: Your order will be subject to the applicable state and local sales taxes. The cost of having food delivered is known as the delivery fee.The cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.Therefore, the cheapest pizza without a delivery fee is 13.25 × and the cheapest delivery fee is $3.75.
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At a simple annual interest rate of 4.5%, how many years will it take Sam to earn $135 interest on an original deposit of $1,000?
A. 3
B. 4
C. 5
D. 6
Answer: A
Step-by-step explanation:
Interest = Principal * Rate * Time
135 = 1000 * 4.5% * T
135 = 1000 * 0.045 * T
135 = 45 * T
T = 135/45
T = 3 (A)
What is the volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square in?
The volume of a triangular pyramid that is 10 in. tall and has a base area of 9 square inches is 30 cubic inches.
Volume of a triangular pyramidTetrahedrons are polyhedra made up of four triangular faces, six straight edges, and four vertex corners. They are also referred to as triangular pyramids.
The given shape is known as a triangular pyramid and the formula for calculating its volume is expressed as:
V = BH/3
where
B is the base area
H is the height of the prism
Determine the base area
B = 1/2 * base * height
B = 9 square inches
H = 10 inches
Substitute the given parameters into the formula
V = 9*10/3
V = 3*10
V = 30 cubic inches
This given the required volume of the prism
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