Answer:
n + 5 = 3(n + 5) where n = -5
Step-by-step explanation:
- 5 more than a number
means adding 5 to a number, n + 5
- equivalent
means equal
- the sum of 5 and the number
- 3 times
sum is addition, n + 5
multiply by 3
3(n + 5)
combine:
n + 5 = 3(n + 5)
want to find n?
n + 5 = 3(n + 5)
n + 5 = 3n + 15
n + 5 - 5 = 3n + 15 - 5
n = 3n + 10
n - 3n = 3n - 3n + 10
-2n = 10
-2n / - 2 = 10 / -2
n = -5
Answer:
The number is:
-5
Step-by-step explanation:
5 + a = 3(5+a)
5 + a = 3*5 + 3*a
5 + a = 15 + 3a
5 - 15 = 3a - a
-10 = 2a
-10/2 = a
a = -5
Check:
5 + (-5) = 3(-5+5)
5 - 5 = 3*0 = 0
79/11 as a mixed number
79/11 as a mixed number is \(7\frac{2}{11}\).
What is an improper fraction?A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.
We have an improper fraction 79/11.
In order to change into improper fraction:
First, we find the whole number.
79/11 = 7.1818181818
79/11 ≈ 7.
Here, 7 is the whole number.
In order to figure this out, multiply the whole number we calculated 7 by the original denominator (11). After that, the outcome of that multiplication is deducted from the initial numerator:
79 - (11x 7)
= 79 - 77.
= 2.
2 is the numerator.
So, 79/11 = \(7\frac{2}{11}\), which is a mixed fraction.
Therefore, the mixed number is \(7\frac{2}{11}\).
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Which of the following lines is perpendicular to y = -2x +3?
A. y= 2x +3
B.
1
y=-x+3
2
C. y=-2x +2
D.
1
= --X-2
2
y=1/2x-2 is perpendicular to y=2x+3
Olivia deposit 6952 in a savings account paying 3.72% interest to the nearest dollar how much money does Olivia have in total after 16 years
There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of acorns to squirrels? Enter your answer in reduced form.
Answer: 1:6
Step-by-step explanation:
Reduce each side of the ratio
Answer:
For every 1 squirrel there are 6 acorns
Step-by-step explanation:
u just divide 18 by 3
What is the length of the midsegment of a trapezoid with bases of length 18 and 28?
The length of the midsegment of a trapezoid with the given bases is.
Answer:
midsegment = 23
Step-by-step explanation:
the midsegment is half the sum of the bases, that is
midsegment = \(\frac{18+28}{2}\) = \(\frac{46}{2}\) = 23
Plz help meeeeeeeeee
Answer:
Step-by-step explanation:
12= 45
14= 45
13=90
angle of a square= 90. 12 and 14 are half of that. 45, 45, 90 triangles can be concluded from this, making 13 90.
A certain coin is a circle with diameter 36 mm. What is the exact area of each side of the coin?
The exact area of each side of the coin is
mm?
Answer:
P=36pi
A=3324pi
Step-by-step explanation:
36 diameter so 18 radius but i dont know about what do you mean by side of the coin is it peremeter?
if it is then it is 36 pi
Area will be 18^2 pi which is 324 pi
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Which equation is represented by the graph?
A:
y= (£-1)+3
B:
4=(¢- 32+1
C:
9=-¢+32_1
D:
4=-¢- 32+1
Answer:
C: y = -(x +3)² -1
Step-by-step explanation:
You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.
Vertex formFor vertex (h, k), the vertex form equation of a parabola is ...
y = a(x -h)² +k
Given that (h, k) = (-3, -1), the equation will have the form ...
y = a(x -(-3))² + (-1)
y = a(x +3)² -1 . . . . . . . . . . matches choice C
The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.
y = -(x +3)² -1
__
Additional comment
Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.
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What are the coordinates of R' for the dilation D(0.5. p)(PQRS)?
Answer:
\(R' = (-1,-0.5)\)
Step-by-step explanation:
See attachment for complete question.
From the attachment:
\(P = (-3,-3)\)
\(R = (1,2)\)
Dilation:
\(D_{(0.5,P)}\)
Required
Determine R'
First, subtract the coordinates of P from R. This means that R is measured from P.
\(R = (1-(-3),2-(-3))\)
\(R = (1+3,2+3)\)
\(R = (4,5)\)
Next, apply dilation factor 0.5
\(R' = R * 0.5\)
\(R' = (4,5) * 0.5\)
\(R' = (4* 0.5,5* 0.5)\)
\(R' = (2,2.5)\)
Lastly, measure R' from the origin by adding the coordinates of P to R'
\(R' = (2+(-3),2.5+(-3))\)
\(R' = (2-3,2.5-3)\)
\(R' = (-1,-0.5)\)
Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.
The coordinate of the R' after the dilation is (-1,-0.5)
What is dilation?Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.
Given information-
The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).
The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,
\(Q'=Q-P\\Q'=(-3-(-3), 2-(-3))\\Q'=(0,5)\)
Similarly,
\(R'=R-P= (1-(-3),2-(-3))=(4,5)\\P'=P-P=(-3-(-3), 3-(-3)=(0,0)\\S'=S-P=(1-(-3),-3-(-3))=(4,0)\\\)
As the dilation factor is 0.5. Thus, the point of Q is,
\(Q"=(0.5)\times(0,5)=(0,2.5)\)
Similarly,
\(R"=(0.5)\times(4,5)=(2,2.5)\\P"=(0.5)\times(0,0)=(0,0)\\S"=(0.5)\times(4,0)=(2,0)\\\)
Add the points P back, to the above coordinate plane to get the dilation point. Thus the point of Q is,
\(Q'''=(0,+(-3), 2.5+(-3))\\Q'''=(-3,-0.5)\)
Similarly,
\(R'''=(2+(-3),2.5+(-3))=(-1,-0.5)\\P'''=(0+(-3),0+(-3))=(-3,-3)\\S'''=(2+(-3),0+(-3))=(-1,-3)\\\)
Thus the coordinate of the R' after the dilation is (-1,-0.5)
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Which crime is often alcohol related?
O a. theft
Ob. tax fraud
O c. trespassing
O d. domestic violence
The crime that is often alcohol related is domestic violence. That is option D.
What is domestic violence?Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.
The causes of domestic violence include the following:
History of violent victimization.Attention deficits, hyperactivity, or learning disorders.History of early aggressive behavior.Involvement with drugs, alcohol, or tobaccoTherefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.
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A fair coin tossed 3 times. What is the probability tossing at least 1 head
Answer:
\(\frac{7}{8}\)
Step-by-step explanation:
Determine g(x-1) for the following function: g(x)=x^2-1
The function opeartion g( x - 1 ) in the function g( x ) = x² - 1 is x² - 2x.
What is the function operation g( x - 1 ) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
g( x ) = x² - 1g( x - 1 ) = ?To solve for g( x - 1 ), replace the variable x in g(x) with x - 1 and simplify.
g( x ) = x² - 1
g( x - 1 ) = ( x - 1 )² - 1
Expand using FOIL Method.
g( x - 1 ) = ( x - 1 )( x - 1 ) - 1
g( x - 1 ) = x( x - 1 ) - 1( x - 1 ) - 1
g( x - 1 ) = x² - x - x + 1 - 1
Collect and add like terms
g( x - 1 ) = x² - 2x + 0
g( x - 1 ) = x² - 2x
Therefore, the function opeartion g( x - 1 ) is x² - 2x.
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You deposit $500 in an investment account. The rate of growth is 6% a year. If you make no further deposits or withdrawals, and the investment is allowed to grow uninhibited, how long will it take for your investment to reach $1,500? Round to the nearest tenth.
A. 18.3 years
B. 45.1 years
C. 27.6 years
D. 8.0 years
With the given compound interest of 6% per year to reach the investment at $1500, it will take 18.3. years thus option (A) is correct.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550.
As per the given,
Principle amount P = $500
Rate of interest r = 6% annually
Total investment = P(1 + r)^T
1500 = 500(1 + 0.06)^T
300 = 1.06^T
Take natural logs on both sides
ln300 = T ln1.06
T = 18.3 years
Hence "With the given compound interest of 6% per year to reach the investment at $1500, it will take 18.3. years".
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16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Elizabeth made a scale drawling of a city of Colorado. The scale of the drawling is 1inch=4 yards.an open space is 17 inches in the drawling. How wide is the actual open space.
Answer:
B
Step-by-step explanation:
Jrkrkr
please help.
definitions: 1. definition of right triangle
2. definition of isosceles TrianglesReflexive
3. HL
4. definition of perpendicular
5. CPCTC
6. reflexive
From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC
How to solve two column proof problems?The two column proof to show that ∠BAC ≅ ∠DAC is as follows:
Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD
Reason 1: Given
Statement 2: AB ≅ AD
Reason 2: Definition of isosceles Triangles
Statement 3: ∠1 and ∠2 are right angles
Reason 3: Definition of perpendicular
Statement 4: AC ≅ AC
Reason 4: Reflexive Property
Statement 5: ΔABC and ΔADC are right triangles
Reason 5: Definition of right triangle
Statement 6: ΔABC ≅ ΔADC
Reason 6: HL Congruency
Statement 7: ∠BAC ≅ ∠DAC
Reason 7: CPCTC
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Tyler made six loaves of pumpkin bread that had 1/4 cup of oil in each loaf. After he was done baking, he had 3/8 cup of oil remaining. How much did he have before baking
Answer:
1.875
Step-by-step explanation:
1/4 times 6= 3/2
3/2 + 3/8 =1.875
hope this helps!
Amanda has three different colored pens in her book bag: blue, green and purple. The probability of randomly choosing a blue pen from Amanda’s book bag is 40%. The probability of randomly choosing a green pen from Amanda’s book bag is 10%.
Suppose Amanda has 20 pens total in her book bag. How many blue pens would Amanda expect to see in her bag?
Answer:
If there are 20 pens in total, and the probability of choosing a blue pen is 40%, then there are 0.4 times 20, or 8 blue pens in Amanda's bag.
Let me know if this helps!
The number of blue pens would Amanda expect to see in her bag is 8.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
In our daily time, there are several instances in the everyday world where we may need to draw conclusions about how everything will turn out.
Total number of pens = 20
Probability of choosing blue pen = 40%
Since,
Probability = Desire item / sample space
So,
Probability of choosing blue pen = Number of blue pens / total number of pen
0.40 = Number of blue pens / 20
Number of blue pens = 0.40 × 20 = 8
Hence "the number of blue pens would Amanda expect to see in her bag is 8".
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Sixth grade > P.9 Add and subtract rational numbers GDR Add.
\( \frac{ - 3 \10{ + }{ - 9 \times \ \frac{910}{?} {?}{?} ?} {?} \)
-
\( \frac{ - 3}{10 } + - 9 \times \frac{9}{10} =\)
The result of the expression (-3/10) + -9 × 9/10 is -42/5
The expression is
(-3/10) + -9 × 9/10
The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.
The expression is
(-3/10) + -9 × 9/10
Here we have to do the suitable arithmetic operations
First do the multiplication in the given expression
= (-3/10) + (-9×9)/10
= (-3/10) + -81/10
Add the terms in the expression
Here the denominator of the both term is equal so we just need to add the numerators
= (-3 + -81) / 10
= (-3 - 81) / 10
= -84 / 10
Divide both numerator and denominator by 2
= -42/5
Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5
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Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.
Answer:
\(=2(2x-5)(x+1)\)
Step-by-step explanation:
So we have the trinomial:
\(4x^2-6x-10\)
First, factor out a 2:
\(=2(2x^2-3x-5)\)
Now, factor within the parentheses.
To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b
(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.
-5 and 2 works. Therefore:
\(=2(2x^2-3x-5)\)
Replace -3x with 2x and -5x:
\(=2(2x^2+2x-5x-5)\)
Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:
\(=2(2x(x+1)-5(x+1))\)
Grouping:
\(=2(2x-5)(x+1)\)
And we're done!
Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (-7,1);m=3
The equation of the line is=
Answer:
The answer is
\(y - 1 = 3(x + 7)\)Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
\(y - y_1 = m(x - x_1)\)
where
m is the slope
( x1 , y1) is the point
From the question the point is (-7,1)
and slope/m=3
The equation of the line is
\(y - 1 = 3(x + 7)\)
Hope this helps you
The probability of a tourist visiting an area cave is 0.70 and of a tourist visiting a nearby park is 0.60. The probability of both places on the same day is 0.40. The probability that a tourist visits at least one of these two places is
The probability that the tourist visits atleast one of the two places is 0.90
Probability of cave visit, P(C) = 0.70
Probability of park visit = P(N) = 0.6
Probability of both = P(B) = 0.40
The probability of visiting atleast one of the two places can be defined thus :
P(Atleast one) = P(C) + P(N) - P(B) P(Atleast one) = 0.70 + 0.60 - 0.40P(Atleast one) = 0.90Therefore, the probability of visiting atleast one of the two places is 0.90
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The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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Brittany asked her classmates: How much time, in minutes, do you spend reading each day? Here are the results: 10, 20, 20, 20, 30, 30, 30, 30, 30, 40, 40, 40, 60, 60, 60 Display the data in a line plot, a histogram, and a box plot. Next to each graph, write down something you notice about the data. Upload your completed plots here.
The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.
Line Plot:
A line plot displays data points on a number line, representing the frequency or count of each value.
In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.
For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.
Histogram:
A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.
The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.
The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.
The height of each bar in the histogram will represent the number of students falling into each interval.
Box Plot:
A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.
The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.
The box will represent the interquartile range (IQR), showing the middle 50% of the data.
The line within the box will represent the median value.
The whiskers will indicate the minimum and maximum values, excluding outliers.
By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.
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Ms. Harrell tells her class that the current Dow Jones Industrial Average, in
expanded form, is:
1x10,000+ 6x1,000+ 3x100+ 7x10+8x1 +9x 1
10
100
Which of the following shows this value in standard form?
Answer: 16,370,89
Step-by-step explanation:
also its 8x 1/10 + 9x 1/100
38. Evaluate the expression
52 - (3²+4)
What is the value of ?
T
80°
25°
R
?
P
PLEASE
9514 1404 393
Answer:
105°
Step-by-step explanation:
The exterior angle marked "?" is equal to the sum of the remote interior angles:
? = 25° +80°
? = 105°
(05.03 LC)
The equation shows the relationship between x and y:
y = −4x + 9
What is the slope of the equation? (5 points)
Group of answer choices
−9
−4
4
9
The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:
Answer:
(a) To find the mean of the data set, sum up all the values and divide by the total number of values.
44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398
Mean = 398 / 8 = 49.75
Rounded to one decimal place, the mean of this data set is 49.8.
(b) To find the median of the data set, i need to arrange the values in ascending order first:
39, 44, 44, 44, 54, 54, 54, 65
The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:
(44 + 54) / 2 = 98 / 2 = 49
Rounded to one decimal place, the median of this data set is 49.0.
(c) To determine the modes of the data set, identify the values that appear most frequently.
In this case, the mode refers to the value(s) that occur(s) with the highest frequency.
From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.