15.0 ( to the nearest tenth )
calculate the distance (d) using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (7, - 4 ) and (x₂, y₂ ) = (- 8, - 5 )
d = √(-8 - 7 )² + (- 5 + 4 )² = √(225 + 1 ) = √226 ≈ 15.0
a day care program has an average daily expense of $75 the standard deviation is $5 the owner takes a sample of 64 bills what is the probability the mean of his sample will be between $70 and $80? The answer choices are 68 1.0 34 + 30. Step 1 calculate a z-score for $70 step to give the probability for Step 1. Step 3 calculate the Z score for $80. Step for give the probability for step 3.
you can use the formula for sample means:
[tex][tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex][/tex]
where m stands for a value of the sample mean.
We are looking for the value, specifically for its two borderline values: 70 and 80
and their cumulative probabilities, p(z(80)) and p(z(70)). The difference p(z(80))-p(z(70))
will give the probability that m falls in the interval [70,80]
So let's get cracking at it:
[tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex]
[tex]z(80) = \frac{80-75}{5 / \sqrt{64}} = 8[/tex]
These are very large values of z. You may notice that any z-table online won't even bother covering range that high - the probabilities for these values are virtually 0 (in the neg case) 1 (in the pos case).
This means that numerically the probability of the sample mean of 64 samples falling within the range of 1 standard deviation is very close to 1
So the answer choice should be 1.0
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would be have saved? Round to the nearest tenths of a mile.
riding directly to the pool would be 4.2 miles, so he would have saved 1.8 miles
If rain is falling at a rate of 2.56 inches per hour, how much rain would you expect after 3.75 hours
If rain is falling at a rate of 2.56 inches per hour, one would expect 9.6 inches of rainfall after 3.75 hours.
Explanation:The question pertains to the calculation of total rainfall when the rate of rainfall and time of rainfall are known.
In this problem, the rate of rainfall is given as 2.56 inches per hour and the time as 3.75 hours. The formula for calculating total rainfall is simply to multiply the rate by the time.So, 2.56 inches/hour * 3.75 hours = 9.6 inches total rainfall.
Hence, if rain is falling at a rate of 2.56 inches per hour, you would expect 9.6 inches after 3.75 hours
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Suppose a pony Express rider was paid 192$ for 12 weeks of work if he was paid the same amount each week,how much was he paid for 3 weeks.
Answer:
$48
Step-by-step explanation:
1. 192/12 = 16
2. 16 * 3 = 48
3. Your answer is 48
192/12 = $16 * 3 = $48. $48 dollars was how much he was paid for 3 weeks.
A hybrid car can get 54 mpg when traveling at an average speed of 40 mph. You travel in this car at that speed for 45 miles to your grandparents’ house. Gas at your nearest station cost $3.23. Use this information to complete the statements. It will take________ Hours to get to your grandparents’ house. Your car will use______gallons of gas on the trip. You will spend________on gas for the trip.
A) The time to travel 45 miles at a speed of 40 mph can be found from ...
... time = distance / speed
... time = (45 mi)/(40 mi/h) = 9/8 h = 1 hr 7 min 30 sec
B) The gas consumption can be found from ...
... (45 mi)/(54 mi/gal) = 5/6 gal
C) The cost of gas can be found from ...
... ($3.23/gal)×(5/6 gal) ≈ $2.69
_____
The units of the numbers tell you what needs to be multiplied or divided to give the answer quantity with correct units. It pays to keep the units with the numbers. They can be treated as though they were a variable.
What is the axis of symmetry for f(x)= 3x^2??
(Three x squared)
the y-axis, that is x = 0
the equation of a parabola in the form f(x) = ax²
has it's vertex at the origin and since the axis of symmetry passes through the vertex then
the axis of symmetry is the y- axis
PLZ HELP FOR BRAINLIEST!!!
The graph of a function is shown:
scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3
Which of the following correctly identifies the set of outputs?
A) {–3, –2, 3}
B) {–1, 2, 3}
C) {(–3, 2), (–2, 1), (3, 3), (3, –1)}
D) {(2, –3), (1, –2), (3, 3), (–1, 3)}
Inputs are the first number output is the second. So youre outputs are 2, -1, -1, and 3. so i would say b
The set of outputs for the function represented by the scatterplot is {-1, 2, 3}, which matches Option B from the given choices.
You are looking to identify the set of outputs (also known as the range) of a given function based on a scatterplot. The output of a function is comprised of the second element in each ordered pair, which represents the y-value on the Cartesian plane. In this case, the scatterplot includes the points (-3, 2), (-2, -1), (2, -1), and (3, 3).
To find the correct set of outputs, we need to list the y-values from each point: 2, -1, -1, and 3. When listing a set, we do not repeat values, so the set of outputs for this function would be {2, -1, 3}. Therefore, the correct answer is Option B) {-1, 2, 3}.
List of the partial product 0f 42 ×28
1,2,3,6,7,14,21,42
1.2,4,7,14,28
The length of a rectangle is three times the width. The area of the rectangle is 108 sq in. What is the width of the rectangle? 6 in. 9 in. 12 in. 36 in.
Let the width of rectangle be X inches
Then according to question
Length of rectangle will be 3X
Also, we know that
Area of rectangle is = L×B
108 = X . 3X
3X^2 = 108
Divide both sides by 3
X^2 = 36
Taking squareroot of both sides
X=6
Therefore, width of rectangle is 6 inches
Answer:
1. 6 in.
Step by step explanation:
Let the width of our rectangle be x inches.
We have been given that the length of our rectangle is three times the width, therefore, length of our triangle will be 3x inches.
We are told that area of the rectangle is 108 square inches.
Since we know that [tex]\text{Area of a rectangle}=\text{Width}\cdot\text{Length}[/tex]
Let us substitute our given information in area formula.
[tex]108=x\cdot 3x[/tex]
Upon multiplying 3x by x we will get,
[tex]108=3x^{2}[/tex]
Let us divide both side of our equation by 3.
[tex]\frac{108}{3} =\frac{3x^{2}} {3}[/tex]
[tex]36=x^{2}[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]6\pm=x[/tex]
Since width cannot be negative, therefore, width of our rectangle will be 6 inches and 1st option is the correct choice.
What number produced the irrational number when added to 1/3
Solution
When we add 1/3 which is rational to an irrational number, we get an irrational number.
pi - is a rational number. √2, √3 are also rational numbers
So the possibilities are pi + 1/3,
2pi + 1/3,
3pi+1/3,
√3 + 1/3,
√2 + 1/3...
I hope this will help you.
Thank you.
Please help! Answer only if you know
area = 20 units²
construct a square of side 6 units around the given figure, then the area of the figure is given by area of square minus 4 congruent triangles
A = 6² - 4 × [tex]\frac{1}{2}[/tex] × 4 × 2
= 36 - 16 = 20 units²
Im begging u, plzzzzzzzz help
a.) Describe a transformation sequence that will transform pentagon ABCDE into pentagon A’B’C’D’E’.
b.) There is more than one way to transform pentagon ABCD into pentagon A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
a) The orientation of the figure ABCDE is clockwise. The orientation of figure A'B'C'D'E' is counterclockwise, so at least one reflection is involved. The direction of AB is North, while the direction of A'B' is West, so a rotation of 90° is involved. Both of these can be accomplished by a reflection across the line that has a direction halfway between these, Northwest. The x-coordinate of point D is the same as that of D', so it is convenient to put point D on the line of reflection.
A transformation sequence that maps ABCDE to A'B'C'D'E' is ...
reflection across the line x+y=-2translation down 2 unitsThe attachment shows the result of reflecting the figure across the line.
b) About any reflection will give the figure the proper orientation. Depending on what it is, some amount of rotation and/or translation may be required.
We can reflect point D across the line y=-2 to put it where point D' is. That reflection changes the direction of AB to South, so we need to rotate the figure 90° CW to get AB to point West. Since we want point D' to be invariant, we can use that point as the center of rotation.
A second transformation that gives the same mapping is ...
reflection across the line y = -2rotation 90° CW about the point (-1, -3)which of the following equations is equivalent to 1/4x -1/2y =8? a) 2x-4y=8. b)2x-4y =64. c) 4x-2y =64
If you multiply the original equation by 8, you get
... 8(1/4x -1/2y) = 8(8)
... 8/4x -8/2y = 64
... 2x -4y = 64 . . . . . matches choice b)
cersei is 3 times older than Arya. In 15 years their combined ages will be 94.How old are each of them now (please show work)
The "work" can be all in your head. In 15 years, their combined ages will have increased by 30 years over what it is now*, so their combined age now must be 64 year. If the ratio of their ages is 3:1, the youngest must be 1/(3+1) = 1/4 of the total, or 16 years.
Arya is 16 years old; Cersei is 48 years old.
_____
* Each person ages one year each year, so their combined age increases by 2 years each year. In 15 years, their combined age will increase by 30 years.
_____
If you insist on an equation, let "a' represent Arya's age. Then 3a represents Cersei's age. The relationship given in the problem is ...
... (a +15) + (3a +15) = 94
... 4a +30 = 94 . . . . . . . . . . collect terms
... 4a = 64 . . . . . . . . . . . . . . subtract 30
... a = 64/4 = 16 . . . . . . . . . multiply by 1/4
This equation and its working should look a lot like the verbal reasoning we did above.
Beth swam laps to raise money for a charity. Beth raised $15 plus $0.65 per lap that she swam. She raised a total of $80. Let x represent the number of laps Beth swam. What expression completes the equation to determine the total number of laps Beth swam? How many laps did Beth swim? Enter your answers in the boxes.
______= 80
______ Laps
The amount Beth raised by swimming is ...
... x · $0.65
In addition, she had a contribution that was not related to the number of laps. Her total can be expressed as
... 15 + 0.65x = 80
_____
Subtract 15 and divide by 0.65 to find
... x = (80 -15)/0.65 = 65/0.65 = 100
Beth swam ...
... 100 Laps
Help please 11, 12, 13
11. {OD, OH} . . . or . . . {OB, OJ}
12. b. Open a compass to distance AB
13. 17 square units
Step-by-step explanation:11. Opposite rays are rays that together make a line. The only point they have in common is their mutual end point.
Given the letter names of points on lines, one can name opposite rays by choosing 3 collinear points, and selecting the middle one of those for the mutual end point. That point's name will be the first letter of each of the ray names. One ray will be named by one of the remaining points, and the other will be named by the other remaining point.
Here, we can choose points H, O, D on the same line. Then rays in opposite directions will be OD and OH, each having point O as its end point.
Similarly, we can choose points B, O, J on the other line and name opposite rays OB and OJ.
___
12. The general sequence of steps for copying a line segment is to draw a line segment longer than the one you want to copy, mark a point on it, set the compass to the length of the given segment, then use the marked point as one end and mark the distance from that point using the compass.
Here, the target line and reference point (C) have been made already, so the next step is open the compass to distance AB.
___
13. The unadulterated triangle has legs of 6 and 8 units, so an area of ...
... area = (1/2)bh = (1/2)(6)(8) = 24 . . . . square units.
One can count the squares within that area that have been removed from the triangle. There are 7 of them, so the area is ...
... 24 -7 = 17 . . . . square units
There are other ways to find the area, including dividing the triangle into smaller pieces. Doing the latter, one needs to be careful, because the slanted side only goes through a grid intersection at points (1, 1), (4, 5), and (7, 9).
If one uses two triangles with legs 3 and 4, and a central rectangle of 2×3, then the area adds up to 6+6+5 = 17 square units, because there is one square taken out of the lower right corner of the upper triangle.
What is the volume of a figure that is filled with 36, 1 inch cubes
It should be no surprise that the volume of a 1-inch cube is 1 cubic inch. Assuming those 36 cubes completely fill the interior volume of the figure, that figure's volume is
... 36 cubic inches
1.994 x 10^-23 1.67 x 10^-24 what are the difference
Answer:
1.827 x 10^-23
Step-by-step explanation:
(1.994 x 10^-23) - (1.67 x 10^-24) = 1.827 x 10^-23
PLZ HELP GEOMETRY BELOW
This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.
Here the problem is justification step 2. The written equation
BC ÷ DC = BC ÷ AC
is incorrect, and wouldn't get us our statement 2, which is correct.
For similar triangles we have to carefully pair the corresponding parts to get our ratios right:
ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.
Justification 2 has the final division upside down.
Based on the diagrams, which statement is true?
Using a somewhat liberal interpretation of "the angles shown in the diagrams", we can conclude that the appropriate choice is ...
... A. The value of x should be 75, because the angles shown in the diagrams are congruent.
_____
There are 8 angles shown in each of 4 diagrams. All 32 angles are not congruent. Taken literally, "the angles shown in the diagrams are congruent" is a false statement. Rather, the marked pair of angles in each diagram are congruent angles.
slope and rate of change
help please on card 7 an 8
Answer:
Card 7
The hourly rate of change/slope is $75 per hour.
Card 8
Frastastic is charging $0.48 per ounce.
Step-by-step explanation:
Card 7
Lets take the set up fee as "$[tex]s[/tex]" and,
Hourly rate as $[tex]x[/tex]per hour.
Now we can write equations for 3 hour event and 5 hour event.
[tex]s+3x=275[/tex] <------- (1)
[tex]s+5x=425[/tex] <------- (2)
Now we need to solve the simultaneous equations to find [tex]s[/tex] and [tex]x[/tex].
Subtract (1) from (2)
⇒[tex]s+5x-(s+3x)=425-275[/tex]
[tex]s+5x-s-3x=150[/tex]
[tex]2x=150[/tex]
[tex]x=75[/tex]
So the hourly rate of change/slope is $75 per hour.
Therefore, Raymond is right.
Card 8
You can take Amount (oz) as x values and Cost as y values and plot a graph.
Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.
Slope of a linear graph is given by the following equation;
Slope(m)=[tex]\frac{y_{1}-{y_{2}}} {x_{1}-x_{2} }[/tex]
Slope(m)=[tex]\frac{6.72-2.4}{14-5}[/tex]
Slope(m)=[tex]\frac{4.32}{9}[/tex]
Slope(m)=[tex]0.48[/tex]
Therefore, Frastastic is charging $0.48 per ounce.
This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.
Can someone please help me with business math
Answer:
1721 $
1612.80
Step-by-step explanation:
Straight line depreciation means depreciation is the same spread over for all the years. The spread over amount is nothing but total cost of equipment - salvage value.
Here we have
Cost of equipment(Purchase cost) ... 18000
Shipping costs ... 620
Installation costs ... 590
Total cost of equipment ... 19210
Less: salvage value at the end ... 2000
Net cost of equipment for 10 years ... 17210
Depreciation per year = Net cost /number of years of life
= 17210/10 = 1721/-
Hence answer is 1721/- for all years and also hence for year 2.
--------------------
Peach tree has an average life of 12 years. First 3 years no benefit would arise, 4 to 8 would be peak and after that slowly decreasing.
Hence in 9th year there would be least value and least depreciation.
Hence answer is $1612.80
Consider the scatter plot.
Describe the outliers from the scatter plot.
the outliers (8,25) and (39,16)
Answer:
The outliers are (8,25), and (39,16)
Step-by-step explanation:
These two points are outliers because they have a great value difference when compared to the other values.
PLEASE ANSWER!! SHOW ALL YOUR WORK!
The perimeter of an isosceles triangle is 7.5m, and the length of a leg is 2m. Find the length of the base.
Answer:
3.5 m
Step-by-step explanation:
The perimeter is the sum of the lengths of the three sides of the triangle, so is the sum of two legs and the base.
... 7.5 m = (2 m) + (2 m) + base
... 3.5 m = base . . . . . . subtract 4 m
base = 3.5m
Since the triangle is isosceles both legs are equal to 2m
base = 7.5 - 2 - 2 = 3.5m
Point A is located at (3,4) and is rotated 90 degrees counterclockwise about the origin. What is the new point of A?
A'(- 4, 3 )
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
A(3, 4 ) → A'(- 4, 3 )
According to the table the investment has doubled in worth by the start of which year?
Answer:
The investment has doubled in worth by the start of 15th year.
Step-by-step explanation:
We are Provided a table which tells us that principal amount of $100 is invested on a interest rate of 5% for 15 years compounded annually and we are asked to find out by the start of which year our investment will be doubled.
We can see that after 14 years our amount is doubled but this can't be our answer as amount is doubled ($207.90) after 14 years not in the start of 14th year. We can see that by the start of 15 year our amount is doubled that is $207.90.
Therefore, by the start of 15th year our investment will be doubled.
Need help with this one please answer fast
how do i wright linear functions
A linear function is the equation of a line. Here, you are given two points on the line, one of which is the y-intercept, and asked to write the equation. It can work reasonably well to use the 2-point form of the equation of a line.
For points (x1, y1) and (x2, y2), the equation of the line through them can be written as
... y = (y2 -y1)/(x2 -x1)·(x -x1) + y1
When it is possible to use x1 = 0, this is simplified somewhat, so we choose
... (x1, y1) = (0, -5) . . . . . . from f(0) = -5
... (x2, y2) = (5, -1) . . . . . .from f(5) = -1
Putting these values in the above formula, we get ...
... y = (-1 -(-5))/(5 - 0)·(x -0) -5
... y = 4/5x -5 . . . . . simplified
This can be put in the desired functional form using f(x) instead of y:
... f(x) = 4/5x -5
Here we're given two points on a line: (0,-5) and (5, -1). Going from the first point to the second, x increases by 5 and y increases by 4. Thus, the slope of the line is
m = 4/5 = 1. Use the point-slope formula to find the equation of this line:
y-(-5) = (4/5)(x). Thus, y = (4/5)x - 5 or f(x) = (4/5)x - 5
Use the x-intercept method to find all real solutions of the equation x^3-6x^2+11x-6
I think that this is the x-intercept method:
First of all, we set y=x^3-6x^2+11x-6.
To find x, we need to let y=0. (y is also equals to f(x))
f(x)=x^3-6x^2+11x-6
In order to make f(x)=0, what does x have to be?
f(1)=0
So then we divide x^3-6x^2+11x-6 by x-1. Why? Because that will not give us a remainder.
(x^3-6x^2+11x-6)/(x-1) = x^2-5x+6
Now, we need to factorize it.
x^2-5x+6 = (x-2)(x-3)
So x=2,3
Which of the following graphs represents an exponential function?
I choose C, but I'm not sure.
The graph which represent a exponential function is:
Graph A.
Step-by-step explanation:Exponential function--
A exponential function is a function which is in the form of:
[tex]y=f(x)=ab^x[/tex]
where a and b are integers and a,b≠0.
Also, the graph of a exponential function either increases continuously or decreases continuously and rapidly in it's domain.The x-axis is always an asymptote for the graph.Also, the path traced by it is not along a straight line.From the given graphs, the graph which one that represents a exponential function is: Graph A.
What is an exponential graph?An exponential graph represents a mathematical relationship where the dependent variable (y) is a constant raised to the power of the independent variable (x). This results in a curved graph that either increases or decreases rapid
A exponential function is a function which is in the form of:
[tex]y = f(x) = ab^{x}[/tex]
where a and b are integers and a,b≠0.
On the other hand, the graph of a exponential function either increases continuously or decreases continuously and rapidly in it's domain.
The x-axis is always an asymptote for the graph.
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