Question 7
Maya, Tom, and Greg sent a total of 153 text messages over their cell phones during the weekend, Greg sent 9 fewer messages than Maya,
Tom sent 4 times as many messages as Greg, How many messages did they each send?
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The messages sent by them are ~
Maya = 33 messages Greg = 24 messages Tom = 96 messages\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)
Let the number of messages sent by Maya be x,
messages sent by Greg = x - 9
messages sent by Tom = 4(x - 9)
and, total number of messages sent by them all together is equal to ~ 153
that is ~
\(x + x - 9 + 4(x - 9) = 153\)\(2x - 9 + 4x - 36 = 153\)\(6x - 45 = 153\)\(6x = 153 + 45\)\(6x = 198\)\(x = 198 \div 6\)\(x = 3 3\)Hence, the messages sent by them are ~
Maya = x = 33Greg = x - 9 = 33 - 9 = 24Tom = 4(x - 9) = 4 × 24 = 96Let Maya send m
Greg send m-9
Tom sent 4(m-9)
ATQ
m+m-9+4(m-9)=1532m-9+4m-36=1536m-45=1536m=153+456m=198m=33Greg=33-9=24
Tom=4(24)=96
Related Questions
Find the point estimate for the true difference between the given population means.
Weights (in Grams) of Soap Bar A: 121, 122, 124, 123, 120, 124, 121, 121, 121, 123, 120
Weights (in Grams) of Soap Bar B: 121, 120, 122, 119, 121, 122, 122, 120, 120, 121, 122, 123, 119
Answers
Answer:
0.9 grams
Step-by-step explanation:
The point estimate for the average weight of Soap Bar A is:
\(A=\frac{121+122+124+ 123+ 120+ 124+ 121+ 121+ 121+ 123+ 120}{11}\\A=121.82\ grams\)
The point estimate for the average weight of Soap Bar B is:
\(B=\frac{121+120+122+ 119+ 121+ 122+ 122+ 120+ 120 +121+ 122+123+119}{13}\\B=120.92\ grams\)
Therefore, the point estimate for the true difference between the given population means is:
\(Dif = A-B\\Dif = 121.82-120.92\\Dif=0.9\ grams\)
The point estimate for the difference is 0.9 grams.
The population of a country is increasing at a rate
of 1.7% per year. By
what percentage does it
increase over 10
years?
Answers
Answer:
17%
Step-by-step explanation:
Solve for y when x = -8. k=-5 y = [?] Remember: y=kx
Answers
PLEASE HELP!!!
which angle is supplementary to
∠1?
A) ∠2
B) ∠3
C) ∠4
D) ∠5
PLEASE LOOK AT THE PICTURE!!!!!
Answers
AREA AND VOLUMEInvestigating the effects on the area for non-proportiona
Answers
(a)
Let:
w1 = Original width
l1 = Original length
w2 = New width
l2 = New length
A1 = Original area
A2 = New Area
so:
\(\begin{gathered} w2=3w1=3\cdot10=30ft \\ l2=2l1=2\cdot50=100ft \\ A2=w2\cdot l2=3000ft^2 \end{gathered}\)Answer:
New length: 100ft
New width: 30 ft
New Area: 3000ft²
-------------------------------------------
(b)
\(\frac{A2}{A1}=\frac{3000}{500}=6\)Answer:
The area of the new walkway will be 6 times the area of the current walkway
---------------------------------------
(c)
\(\begin{gathered} 8\cdot500=x\cdot50\cdot4\cdot10 \\ 4000=2000x \end{gathered}\)Solve for x:
\(\begin{gathered} x=\frac{4000}{2000} \\ x=2 \end{gathered}\)Answer:
Make the new length 2 times the current length.
what is the smallest angle of a right triangle with sides 9, 40, and 41? Round your answer to the nearest degree.
Answers
Answer:
13°
Step-by-step explanation:
The smallest angle in a triangle is the angle opposite the shortest side.
In this case the angle opposite side 9
let the angle be x, then using the tangent ratio in the right triangle
tan x = \(\frac{opposite}{adjacent}\) = \(\frac{9}{40}\) , thus
x = \(tan^{-1}\) (\(\frac{9}{40}\) ) ≈ 13° ( to the nearest degree )
A university student is selecting courses for his next semester. He can choose from 8 science courses and 4 humanities courses. In how many ways can he choose 4 courses if more than 2 must be science courses
Answers
The number of ways which he can choose 4 courses if more than 2 must be science is; 224 ways.
Combination of outcomes;
He can choose from 4 humanities courses and 8 science courses.
If the condition requires that he chooses more than 2 science courses, it follows that;
He can only choose three science courses and only 1 humanities courses.
8C3 x 4C1 = 56x 4 = 224
On this note, the number of ways he can choose the required 4 courses is; 224 ways.
Learn more on combination here:
brainly.com/question/4658834
#SPJ1
Chelsea bought a computer on Monday for $1,300. Its value is predicted to decrease by $250 per year. Her brother George also bought a computer on Monday. The function g(x) = 1,100 – 175x predicts how the value of his computer is expected to change after x years.
Whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be?
A) Chelsea’s computer is expected to have a value of $25 greater.
B) George’s computer is expected to have a value of $25 greater.
C) Chelsea’s computer is expected to have a value of $125 greater.
D) George’s computer is expected to have a value of $125 greater.
Answers
Answer:
The correct answer is B. George’s computer is expected to have a value of $25 greater.
Step-by-step explanation:
Since Chelsea bought a computer on Monday for $ 1,300, and its value is predicted to decrease by $ 250 per year, while her brother George also bought a computer on Monday, and the function g (x) = 1,100 - 175x predicts how the value of his computer is expected to change after x years, to determine whose computer is expected to have a greater value when it is 3 years old, and how much greater will it be, the following calculation must be performed:
Chelsea:
1,300 - (250 x 3) = X
1,300 - 750 = X
550 = X
George:
1,100 - (175 x 3) = X
1,100 - 525 = X
575 = X
Therefore, George’s computer is expected to have a value of $ 25 greater.
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
Answers
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
Find out more on domain here: https://brainly.com/question/26098895
#SPJ1
In the square pyramid shown, points and are midpoints of the edges of one face. If the figure is sliced through points and and through the base, which best describes the shape of the resulting cross section? The picture shows a triangular prism. M and N are the points on the prism. A. rectangle B. trapezoid C. quadrilateral D. parallelogram
Answers
Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D
Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.
Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.
Therefore, the correct answer is D. parallelogram.
It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.
For more such questions on midpoints visit:
https://brainly.com/question/28667736
#SPJ8
HELP ASAP WILL MARK U BRAINLIESTTTT
Answers
Answer:
125q^6p^3
Step-by-step explanation:
Plz help (extra points)
Answers
Answer:
6/18 bags
Step-by-step explanation:
Answer:
8/12 OF A BAG IS THE RIGHT ANSWER
bought for 15$ sold for 49.50, what is markup percentage?
Answers
Answer:
17.65%
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve
Dilations: Triangle RST with vertices R(-5,1), S(-3,4), and T(2,-1): k=2
Answers
Answer:R’ (-10,2) S’(-6,8) T’(4,-2)
Step-by-step explanation:
Did it in class
After dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).
Given that, ΔRST with vertices R(-5,1), S(-3,4), and T(2,-1).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
Given, scale factor is k=2.
So, with using scale factor
R(-5,1)→2(-5, 1)= R'(-10, 2)
S(-3,4)→2(-3,4)=S'(-6, 8)
T(2,-1)→2(2,-1)=T'(4, -2)
Therefore, after dilation of ΔRST with the given scale factor we have vertices of ΔR'S'T' as R'(-10, 2), S'(-6, 8) and T'(4, -2).
To learn more about the dilation visit:
https://brainly.com/question/13176891.
#SPJ2
Find the number of ways of
arranging the letters of the
words DANGER, so that no vowel
occupies odd place.
Answers
Answer: 6 * 24 = 144 ways.
Step-by-step explanation:
Solution:
Given word => DANGER.
The condition is that vowels can't occupy odd places so, we will let them occupy even places.
A total number of arrangements will be = 6 * 24 = 144 ways.
Answer: 6x24 = 144 ways.
divide 360 in the ratio 1:7
Answers
Answer:
45:315
Step-by-step explanation:
Add up the ratio to get the total ratio.
1+7=8
Divide the 360 by the total ratio.
360÷8=45
The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.
1×45=45
7×45=315
so,
45:315
Hope this helped. Comment below if you need more assistance! :)
ax + b2 = cx + d2
????
Answers
Answer:
x=b^2+d^2/a-c
Step-by-step explanation:
derrick is preparing to submit his taxes. over the year, he kept track of certain deductions he is able to claim (all rounded to the nearest dollar). these values are given below. 65,144,97,144,103,98,101,127,58,151 derrick figures that he will receive the following amounts: $25 for each deduction that is under $130 and $45 for each deduction that is $130 or more. use the ti-83 or 84 to draw a histogram for these values using 4 classes. using that histogram, determine how much total derick will receive from all of his deductions.
Answers
Derrick will receive total of $340 from all of his deductions
To create a histogram for these values using four classes, we must first determine the class width, which is determined as the data range divided by the number of classes. The data range is 151 - 58 = 93, which is the difference between the biggest and smallest numbers. The breadth of the class is 93/4 = 23.25. We'll round it up to 24 because we can't have a fractional class width.
Then, for each of the four classes, we'll start with the smallest number (58) and add the class width (24) again until we reach the maximum value (151). The lowest class boundaries for the four classes are as follows:
Class 1: 58
Class 2: 82
Class 3: 106
Class 4: 130
We'll determine the upper class limit for each lower class limit by adding the class width (24) - 1. The upper class restrictions are as follows:
Class 1: 81
Class 2: 105
Class 3: 129
Class 4: 153
Finally, we'll tally the amount of deductions made in each class and utilise that data to create the histogram. Each class has the following number of deductions:
Class 1: 1 (58)
Class 2: 3 (97, 98, 101)
Class 3: 3 (103, 127, 144)
Class 4: 3 (144, 151, 65)
We can compute the total amount Derrick will earn from all of his deductions now that we know the number of deductions in each class. He will earn $25 for each deduction of less than $130, and $45 for each deduction of $130 or more.
Derrick will receive the following total from all of his deductions:
$25 * 1 (for the single deduction of less than $130) + $45 * 7 (for the seven deductions of $130 or over) = $25 + $315 = $340
For more such questions on Histogram, click on:
https://brainly.com/question/25983327
#SPJ4
Jada ran 3 km las weekend which is 15% of the total distance that she will need to run for her long distance race.How many km are in her long distance race?
With an explanation.
Answers
Answer:
20 km
Step-by-step explanation:
if 15 percent is equal 3
then 5 percent is equal 1
if 15 * 6 = 90
and 10 percent equal 2
then 90 percent + 10 percent = 100 percent
6*3=18
18+2=20
so she needs to run 20 km for her long distance race .
Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
Answers
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
For more such questions temperature,click on
https://brainly.com/question/25677592
#SPJ8
7/14 reduced to its lowest form
Answers
Answer:
1/2
Step-by-step explanation:
7 and 14 have a common factor of 7. So divide both by 7 to get 1/2
Answer:
I'm no expert but I think it's 1/2.
Step-by-step explanation:
Divide 7 by 7 and 14 by7
What is the equation of the following line?
Answers
Hope this helped.
Make r the subject of t ＝6r^2 + 12t
Answers
\(\sf \dashrightarrow t = 6r^2 + 12t\)
\(\sf \dashrightarrow -6r^2 = 12t-t\)
\(\sf \dashrightarrow -6r^2 = 11t\)
\(\sf \dashrightarrow 6r^2 = -11t\)
\(\sf \dashrightarrow r^2 = -\dfrac{11t}{6}\)
\(\sf \dashrightarrow r = \pm \sqrt{-\dfrac{11t}{6} }\)
\(\dashrightarrow \sf r=\pm i\sqrt{\dfrac{11t}{6}}\)
Rachel is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove to get to the safe zone at 242424 meters per second. After 444 seconds of driving, she was 707070 meters away from the safe zone.
Let yyy represent the distance (in meters) from the safe zone after xxx seconds.
Complete the equation for the relationship between the distance and number of seconds.
Answers
The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.
Find the equation for the relationship between the distance and number of seconds:A linear function containing one dependent and one independent variable.
It can be represented using the equation,
y = mx + c
where m is the slope
It is given in the question that,
Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.
After 4 seconds of driving, she was 70 meters away from the safe zone.
Let, D(t) be the distance to the safe zone (measured in meters) and t be the time (measured in seconds)
After 4 seconds of driving, she was 70 meters away from the safe zone.
⇒ This means that at t = 4 seconds, D(4) = 70 meters
Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative
⇒ m = - 24
y = mx + c
⇒ D(t) = (-24)t + c
Put t = 4,
D(4) = (-24)4 + c
70 = -96 + c ⇒ c = 166
⇒ D(t) = 166 - 24t
Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.
Learn more about linear function here:
brainly.com/question/13919345
#SPJ1
A polygon with an area of 10 square inches is dilated by a scale factor of 4, what is the new area?
Answers
The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.
Factor the trinomial by grouping. -
8x²2² +14x+3.
a. Find two numbers whose product is 8.3=24 and whose sum is 14.
b. Write 14x using the factors from part (a).
c. Factor by grouping.
Answers
a. The two numbers whose product is 24 and whose sum is 14 are 6 and 4
b. 14x = 6x + 8x
c. 8x²2² + 6x + 8x + 3
=8x²2² + (6x + 8x) + 3
=8x²2² + 14x + 3
The trinomial 8x²2² + 14x + 3 can be factored by grouping as (8x²2² + 14x) + 3
Terri buys five and seven-eighths ounces of chocolate chips. She uses four and four-sixths ounces in a recipe. How many ounces of chocolate chips does she have left?
Answers
Answer:
1 5/24 ounces--------------------------
Find the difference of the initial and used amounts:
5 7/8 - 4 4/6 = 5 - 4 + 7/8 - 4/6 = Combine whole and fraction parts1 + 7/8 - 2/3 = Simplify1 + 21/24 - 16/24 = Common denominator is 241 + 5/24 = Convert to mixed fraction1 5/24Biological agents are measured in
Answers
Answer:
Biological agents are measured by the based or collection of aerosols.
Hope it helps.
54/10 converted to mixed number simply if needed ANSWER QUICK
Answers
Answer:
54/10= 5,4 but if you want to a simple broken number it is 27/5
Two angles form a linear pair. The measure of one angle is (4y + 54)∘and the other angle is (2y + 90)∘. Find the measures of each angle. Do not include any units
Answers
The measure of each of the linear angle pair are: \(78^{\circ} $ and $ 102^{\circ}\)
The linear pair angles have been illustrated in the image attached below.Recall:Angles of a linear pair add up to give us the sum of 180 degrees. Therefore, the sum of the two angles that form the linear pair in the image attached below will equal 180 degrees.
Thus:\((4y + 54) + (2y + 90) = 180\\\)
Solve for the value of y in the equation\(4y + 54 + 2y + 90 = 180\\\\\)
Add like terms\(6y + 144 = 180\\\\\)
Subtract 144 from both sides\(6y = 180 - 144\\\\6y = 36\)
Divide both sides by 6\(y = 6\)
Find the measure of each angle by plugging in the value of y in each expression:
\((4y + 54) = 4(6) + 54\\\\= 24 + 54\\\\= 78^{\circ}\)
\((2y + 90) = 2(6) + 90\\= 12 + 90\\\\= 102^{\circ}\)
Therefore, the two angles that form the linear pair are:
\(78^{\circ} $ and $ 102^{\circ}\)
Learn more about linear pair here:
https://brainly.com/question/12040176
