Answer:
John = 41 years
Sam = 32 years
Step-by-step explanation:
Find the mean of the following group of numbers: 6. 1, 5. 9, 4. 2, 5. 9, and 10. 7. Round your answer to the nearest tenth
Answer:
6.6
Step-by-step explanation:
the "mean" of a data set is what we commonly refer to as the average. We find this estimate of values by adding up all of the values of the data set, and then dividing by the number of values we added together.
{for example: the mean [average] of 1, 5, 6:
1 + 5 + 6 = 12
12 ÷ 3 [we have 3 numbers] = 4}
our values:
6.1 ; 5.9 ; 4.2 ; 5.9 ; 10.7
> 6.1 + 5.9 + 4.2 + 5.9 + 10.7 = 32.8
[we have 5 numbers]
32.8 / 5 = 6.56
when rounding a number, we look to the digit one place to the right. If it is greater than or equal to 5, we "round up" our digit [we move it up to the next digit]
if it is less than 5, we keep our digit the same
(the tenths place = _ . _ _ _ ones. tenths)
so if we round 6.56 to the nearest tenth:
6.56
[6 > 5]
6.6
So, the mean of this data set rounded to the nearest tenth is 6.6
hope this helps!!
Looking for a step by step explanation for this question! I take the Math QRAS Accuplacer soon and practicing my math skills but I seem to be stuck on this problem.
To raise money for their school play, Beatrice sold brownies for $1.25 each, and Chuck sold cookies for $0.75 each. Together, they sold 87 items and made $80.75. How many cookies did Chuck sell?
(A) 15 cookies
(B) 26 cookies
(C) 56 cookies
(D) 65 cookies
The Johnsons’ new swimming pool measures 3x^2-2x+1 ft in length and x+2 ft in width. What is the area of the new swimming pool, in square feet?
Answer:
[tex]3x^3 + 4x^2 -3x + 2[/tex]
Step-by-step explanation:
The area of the swimming pool will be equal to [tex]length * width[/tex].
We know that the length is [tex]3x^2-2x+1[/tex] and the width is [tex]x+2[/tex].
Therefore we can substitute those into the equation:
[tex](3x^2-2x+1)(x+2)\\[/tex]
Then, we expand the brackets using a grid (attached).
After this, we collect like terms to find the final answer:
[tex]3x^3+6x^2-2x^2-4x+x+2\\3x^3 + 4x^2 -3x + 2[/tex]
Our final answer is: [tex]3x^3 + 4x^2 -3x + 2[/tex]
For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?
for the point (16,12) find sin theta and cos theta
Answer:
sinθ = 3/5cosθ = 4/5
Given Point (16, 12) To find Sine and cosine of the angle, using the given coordinatesSolution
Since both of the coordinates are positive, we have:
the angle θ is in the first quadrant, both sine and cosine have positive values;the x-coordinate determines the value of adjacent leg;the y-coordinate determines the value of opposite leg.Find the hypotenuse of the right triangle using values of both legs:
[tex]h=\sqrt{ x^2+y^2}=\sqrt{16^2+12^2}= \sqrt{400} =20[/tex]Find sine:
sine = opposite/hypotenusesinθ = 12/20 = 3/5Find cosine:
cosine = adjacent/hypotenusecosθ = 16/20 = 4/5Which expression is equivalent to startfraction (4 p superscript negative 4 baseline q) superscript negative 2 baseline over 10 p q superscript negative 3 baseline endfraction? assume p not-equals 0, q not-equals 0.
The given expression is equivalent to [tex]\frac{p^{7}q}{160}[/tex]
What are indices?
An index is a small number that tells us how many times a term has been multiplied by itself.
The plural of index is indices.
Below is an example of a term written in index form :[tex]4^{3}[/tex]
4 is the base and 3 is the index.
We can read this as ‘4 to the power 3’
Another way of expressing [tex]4^{3}[/tex] is
4 x 4 x 4 = 64
Indices can be positive or negative numbers.
Given expression can be written as [tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
Now to simplify the given fractional expression :[tex]\frac{({4p^{-4}q})^{-2}}{10pq^{-3}}[/tex]
= [tex]\frac{4^{-2}p^{8}q^{-2}}{10pq^{-3}}[/tex] By using the property of exponents is given by:
[tex](a^{m})^{n}=a^{m n}[/tex]
=[tex]\frac{p^{7}q}{10 .16}[/tex] By using the property of exponents given by
[tex]a^{m}a^{n}=a^{m + n}[/tex] and [tex]a^{-m}= \frac{1}{a^{m}}[/tex]
= [tex]\frac{p^{7}q}{160}[/tex]
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There are 15 men and 21 women in a club. One man and one female are to be selected at random to represent the club. How many different pairs are there?
Someone please help me with this one, thanks
There are 315 number of different pairs
How to determine the number of pairs?The given parameters are:
Men = 15
Women = 21
The number of different pairs is calculated as:
Pair = Men * Women
So,we have:
Pair = 15 * 21
Evaluate
Pair = 315
Hence, there are 315 different pairs
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Draw the graph of f(x) = (x − 1)2 − 2. Start by creating a table of ordered pairs for the function. Then plot the points from the table, and draw a curve connecting the points.
The attached graph represents the graph of f(x) = (x - 1)^2 - 2
How to plot the graph?The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
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Which statement best explains the relationship
between lines AB and CD?
They are parallel because their slopes are equal.
• They are parallel because their slopes are negative
reciprocals.
They are not parallel because their slopes are not
equal.
They are not parallel because their slopes
are
negative reciprocals.
Answer:
They are parallel because their slopes are equal.
Step-by-step explanation:
See attached image.
Find the missing term or terms in each arithmetic sequence.
4) ..., 27,__,__,__, 43, ...
I need help again please!!!!!!
Answer:
I believe the terms would be 31, 35, 39.
Step-by-step explanation:
We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!
An angle is bisected, forming two new
angles. If the original angle had a measure
of 48 degrees, what is the measure of each
new angle?
First let's define bisected
To bisect an angle means to split an angle exactly in half. Both sides of a bisected angle are equal to each other
The original angle (48 degrees) is bisected so we must divide 48 by 2 to find a degree of each angle
48 ÷ 2 = 24
The measure of each new angle is 24 degrees
X. y
-6. -7
.1. 1
0. 9
3. -2
What is the domain of the given function?
(x|x = -6, -1, 0, 3}
(y|y) =-7.-2, 1, 9}
(x|x = -7, -6, -2.-1, 0, 1, 3, 9}
(y|y)= -7, -6, -2, -1, 0, 1, 3, 9}
Answer: Option (1)
Step-by-step explanation:
The domain is the set of input values, also known as the set of x-values.
please help me aspa
Answer:
i's 20 because it seems that it is the most successful
Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 4300(0.042)
X
The change is decay and the percentage rate of decrease will be 95%.
An exponential function is a function where a number is raised to the variable i.e. base is raised to the exponent times.
Here given the exponential function is y= 4300(0.042)ˣ
Now we have to identify if the change in exponential function represents growth or decay, and have to determine the percentage rate of increase or decrease.
Here in the exponential function, the base is less than 1 so the change is decay.
The equation represents exponential decay because the decay factor is lesser than 1.
The general form of the exponential equation is:
y(x)= a(1-r)ˣ such that r is the decay.
equating with the equation
y= 4300(0.042)ˣ
a= 4300
and 1-r=0.042
⇒r= 1-0.042
⇒r= 0.958
the perecentage of decay will be r*100= 0.958*100= 95%
Therefore the change is decay and the percentage rate of decrease will be 95%.
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Consider the transformation shown. 2 triangles are shown. The first is labeled pre-image and the second is labeled image. Both triangles have congruent angle measures. The pre-image has side lengths of 6, 10, and 8. The image has side lengths of 3, 5, and 4. Use the drop-down menus to complete the sentence. The transformation is because the preserved
The transformation is nonrigid because the segment lengths are not preserved.
How to determine the transformation?The image related to the question cannot be found. However, the question can still be solved
The given parameters are:
Triangle 1: 6, 10 and 8Triangle 2: 3, 5 and 4From the question, we understand that the side lengths are not equal.
This means that the triangles are dilated.
And the scale factor of dilation is
Scale factor = 6/3 = 10/5 = 8/4
Scale factor = 2
The scale factor of dilation is 2
Dilation is a non rigid transformation.
Hence, the transformation is nonrigid because the segment lengths are not preserved.
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Answer:
The transformation is nonrigid because the segment lengths are not preserved.
A driver travels the first 240 km of a 600-km journey at an average speed of 60 km/h. If the time taken for the whole journey is 8 hours 48 minutes, find the average speed for the remaining journey.
Step-by-step explanation:
1)Take the time he is traveling divided by the speed to get the time.
2)Subract the time you have got from the average time,then subtract the average distance from the traveling distance,then divide the two to get the speed.
3)Take the total distance, divide it by the total time to get the average speed.
i need quick help on this, please
The coordinates of a point located on the grid is (64.65, 12.4).
We need to find the coordinates of the point given on the grid.
What are coordinates?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Now, from the given grid we can see that the point is located at (64.65, 12.4)
Therefore, the coordinates of a point located on the grid is (64.65, 12.4).
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Which is equivalent to 4√9 1/2x?
Answer:
second branch..................
constant equality 123
Answer:
using the identity (a±b) ² = a² + b² ± 2ab1) X² + 1 - 2X
2).x² + 4 - 4x
3) 9 + x² - 6x
4) y² + 16 - 8y
5) 4x² + 1 - 4x
6) 9 + 4y² - 6y
7) 4x² + y²- 8y
8) 1 + 16a² - 8a
9) 9x²+ 4y² - 12xy
10) -x²- 16y² + 8y
11) -x²- 25y + 10xy
Can someone take a look at this image and answer please!
The answers to the following question is
1) KL = 10
2) TE= 15 cm
3) angle PUT= 13
4) angle SQP = 21
What is similarity in triangle?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
1) Using similarity property in given triangle
SR/ KI= SJ / JK
AS, JK= 2 SJ
SR/ KI= SJ / 2 SJ
5/ KI = 1/2
KL= 10
2) As, the diagonal of parallelogram bisect equally each other then
VE = TE
AS, VE = 15
So, TE= 15 cm
3) As, PU is the bisector of angle SUT
angle PUT= 1/2 (angle SUT)
PUT = 1/2 (26)
angle PUT= 13
4) As PQ is the bisector SQR
angle PQR= angle SQP = 21
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Find the equation of the line of best fit and the correlation coefficient for the data shown.
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
Regression equation:
Using a calculator, we have that:
The regression equation is given by: y = -4.75x + 88.57143.The correlation coefficient is given by: -0.906.How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that:
The values of x are: 1, 2, 3, 4, 5, 6, 7.The values of y are: 88, 75, 71, 69, 66, 68, 50.Hence the regression equation is:
y = -4.75x + 88.57143.
Also using a calculator, the correlation coefficient is of -0.906.
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HELP MOI
MATH WORK=IMPOSSIBLE
PLEASE
Answer:
-32/21
Step-by-step explanation:
First, we can convert -0.35 into a fraction: -35/100, which could be further simplified to -7/20.
Dividing a fraction by another is the same thing as multiplying a fraction by the reciprocal (denominator over numerator) of the fraction. Therefore, we can rewrite this expression as: 8/15 * -20/7
To find the answer to that, you simply multiply the numerators together and the denominators together separately. The final answer is -32/21.
Answer:
-1 11/21
First step:
First, you change the decimal into a fraction. To do that you look at the decimal place at the end of -0.35. The decimal place is hundredths. That means the fraction form of -0.35 is -35/100.
Now to simplify it just find out what both the numbers can be divided by. In this case, 35 and 100 can be divided by 5. If you divide them both by 5 you get -7/20
Fraction form: -7/20
Second step:
Now you just plug it in to the equation.
8/15÷(-7/20)
To solve this you need to change it to multiplication and flip the second fraction.
8/15×(-20/7)
Final step:
Now you multiply the fractions.
8/15×(-20/7)= -32/21 or -1 11/21
Final answer: -1 11/21
help honestly MARKING BRAINLIESt
Answer:
See below ~
Step-by-step explanation:
a) Forming the equation :
⇒ We start with a number, x
⇒ Now we double it so : 2(x) = 2x
⇒ Then we add 11 to it : 2x + (11) = 2x + 11
⇒ It is equal to 25 : 2x + 11 = 25
b) Solving the equation :
Subtract 11 from both sides :
⇒ 2x + 11 - 11 = 25 - 11
⇒ 2x = 14
Divide 2 on both sides :
⇒ 2x/2 = 14/2
⇒ x = 7
Let unknown number be x
Double it
2xAdd eleven
2x+11You got 25
2x+11=25Lets solve the equation
2x=25-112x=14x=7A jacket is on sale for 70% of the original price.if the discount saves $140,what was the original price of the jacket
Answer:
$200
Step-by-step explanation:
Consider the original price be x
As per the question
⇒x×70%=140Solving the equation yields:
⇒0.7x=140⇒0.7x/0.7=140/0.7⇒x=1400/7⇒x=200In conclusion
the original price of the jacket was $200
The solutions to a quadratic equation are x=4 and x=3/5. What is the original equation?
Which of the following angles are congruent?
L
»
M
0
»
O
ZMOL = ZMON
O ZMNO = ZLOK
OZLKO ZNMO
K
N
Answer:
LKO = NMO
Step-by-step explanation:
This is because both of the angles lie on the same "vertical angle", the line segment that connects M to K. The segment MN is also parallel to segment LK. If you have two congruent line segments, then the measure of the angles are congruent.
been having this question for a while and this app wont help
Answer:
b
Step-by-step explanation:
eq y=x+4 is for x>=2 inclusive
Which calculation correctly uses prime factorization to write square root of 48 in simplest form?
The simplest form of the square root of 48 is 4√3
Simplifying rational functionsGiven the following rational function √48
The correct prime factorization is given as;
√48 = √3×16
√48 = √16 × √3
Since the square root of 16 is 4, hence;
√48 = 4√3
Hence the simplest form of the square root of 48 is 4√3
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The students in Class A and Class B were asked how many pets they each have. The dot plots below show the results.
Students in Class A
A dot plot titled Students in Class A. A number line going from 0 to 5 labeled Number of pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Students in Class B
A dot plot titled Students in Class B. A number line going from 0 to 5 labeled Number of pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
What is the difference between the ranges in the dot plots?
0
2
3
4
Unmark this
Answer:
The difference between the Ranges in the dot plots is 2.
Explanation:The range is the distinction between the greatest or highest value and the minimum or lowest value.I've included a figure with the two-dot plots explained for easier comprehension.
Students from Class A.
The value on the far left of the numbered line that contains at least one point is the minimum value for students in Class A, and the maximum value is three (the value to the extreme right of the numbered line that contains, at least, one point).
Range = 3 - 0 = 3
Students from Class B.The value to the far left of the numbered line that has at least one point is the minimum value for students in Class B, and the maximum value is 5. (the value to the extreme right of the numbered line that contains, at least, one point).
Range = 5 - 0 = 5
Variations in the rangesThe dot plots' range differences are 5 - 3 = 2, which is a difference of two.
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The distance between points (x₁, y₁) and (4, 8) is the square root of
(x₁ - 8)² + (₁-4)².
True or False?
The statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)². Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
WE have been given two points.
So,
The distance between points (x₁, y₁) and (4, 8)
D = √[(x-p)² + (y-q)²]
D = √[(x₁-4)² + (y₁-8)²]
But the statement is given as the distance between points (x₁, y₁) and (4, 8) is the square root of (x₁ - 8)² + (₁-4)².
Hence, the given statement is false, it is √[(x₁-4)² + (y₁-8)²].
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PLS HELP ME AND PLEASE GIVE ME THE ANSWER EXPLAINED THANK YOU!!
The coordinates of the vertices of the reflected image are (-3,4) (0,4) (-3, 2) (0,2).
What is reflection?Reflection is a mathematical transformation of a shape by moving the vertices of the shape across a line of reflection.
Analysis:
coordinates of the shape before transformation are: (-3, 0) (0,0) (-3, -2) 0, -2)
Across the line of transformation, the corresponding vertices(old and new) must be equal distance from the line of reflection.
Also for reflection on y-axis only y-coordinates are affected.
so for point(-3, 0) 0 is 1 unit away from y = 1 so the other coordinate 1 unit away from y = 1 is y = 2 making the new point (-3, 2) same as others .
Find the image in the attached file below.
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