[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
Which graph represents the solution of -3m < 15?
Hayley's fuel bills for her house increased from £76 a month in 2021
to £89 a month in 2022. Calculate the percentage increase in Hayley's
fuel bills from 2021 to 2022.
Give your answer correct to three significant figures.
The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.
What is a Percentage Increase?
The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.
Steps to Calculate Percentage Increase?
The formula to calculate Increase (I) is given by, [tex]I=Y-X[/tex], where [tex]X[/tex] is the original value and [tex]Y[/tex] is the new value.The percentage increase formula is given by, [tex]\%I=\frac{I}{X} \times 100[/tex]Here, in the question, it is given that,
The original amount (X) or the fuel bill in 2021 is £76.
The new amount (Y) or the fuel bill in 2022 is £89.
So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,
[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]
Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,
[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]
Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.
To learn more about Percentage Increase from the given link
https://brainly.com/question/28398580
#SPJ1
Use the number line to plot –3, 1, and 3.
Which statements are true
Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.
The correct statements regarding the number line are given as follows:
1 < 3.–3 < 1.How to plot an integer number on the number line?Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.
These numbers are plotted marking a symbol such as a X or a circle on the number line.
The number line is increasing, so the negative numbers appear before the positive numbers.
This means that if a number a is to the left another number b, the number a is less than b, hence:
1 < 3–3 < 1.As the order in which the numbers appear is given as follows:
-3, 1 and 3.
More can be learned about the number line at https://brainly.com/question/28761820
#SPJ1
35. Rosa plants rows of flowers with exactly the same number
in each row. Each row has more than one flower. She has
28 flowers. What is the largest number of rows she can make?
A 4
B
7
12
D 14
Answer: 10 rows of rose plants
Step-by-step explanation:
The number of rose plants in first, second third,..., and last row are respectively.
23,21,19,....,5.
number of rose plants: n
The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n
=a+(n−1)d
⟹5=23+(n−1)×−2
⟹5=23−2n+2⟹20=2n⟹n=10
(PLEASE OPEN) Need help with triangle proofs.
The missing terms in the two column proof are;
Reason 1; Perpendicular bisector
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Reason 4; Reflexive Property of Congruence
Reason 5; Definition of Isosceles Triangle
Reason 6; AAS Congruency Postulate
How to carry out two column proof of triangles?From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC
Now, we have the two column proof as follows;
Statement 1; AO ⊥ BC
Reason 1; Perpendicular bisector
Statement 2; ∠AOB and ∠AOC are right angles
Reason 2; Definition of perpendicular bisector
Statement 3; CO ≅ BO
Reason 3; Segment division
Statement 4; AO ≅ AO
Reason 4; Reflexive Property of Congruence
Statement 5; AB ≅ AC
Reason 5; Definition of Isosceles Triangle
Statement 6; ΔAOB ≅ ΔAOC
Reason 6; AAS Congruency Postulate
The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.
Read more about two column proof at; https://brainly.com/question/1788884
#SPJ1
m∠M = 6x – 6 and m∠P = 4x + 10, what is m∠M?
The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Using the circle graph, the costs to attend the public university are as follows:
cost of tuition and fees = $ 5992.93cost of room = $5115.92cost of board = $ 4044.01computer cost = $1088.15How to find cost using circle graph or pie chart?A circle graph, or a pie chart, is used to visualize information and data.
Therefore, the circle graph is shows the percentage cost for tuition/fees, room, board, and computer costs.
The cost to attend a public university in a recent year is $16,241.
Using the pie chart, let's find the cost of the various fees.
Therefore,
cost of tuition and fees = 36.9% of 16,241
cost of tuition and fees = 36.9 / 100 × 16241
cost of tuition and fees = 599292.9 / 100
Therefore,
cost of tuition and fees = $ 5992.929
cost of room = 31.5% × 16241
cost of room = 31.5 / 100 × 16241
cost of room = $5115.915
Hence,
cost of board = 24.9% of 16241
cost of board = 24.9 / 100 × 16241
cost of board = $ 4044.009
Hence,
computer cost = 6.7% of 16241
computer cost = 6.7 / 100 × 16241
computer cost = $1088.147
learn more on circle graph(pie chart) here: https://brainly.com/question/24207368
#SPJ1
7. Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q + 16,000.
a. Express the expense function in terms of p.
b. At a price of $10.00, how many widgets are demanded?
c. How much does it cost to produce the number of widgets from part b?
I am so confused on how to answer these 3 sections, so if anyone could help I would really appreciate it!!
a. The expense function in terms of p is - 280p + 34, 000
b. At a price of $10.00, 7, 600 widgets are demanded
c. It costs $31, 200 to produce the number of widgets from part b
How to determine the valuesWe have that;
The demand function is q = -140p + 9,000The expense function is E = 2.00q + 16,000To express the expense function in terms of p, we have to take the following steps;
Substitute the value of q in the demand function into the function for the expense, we get;
Expense function = 2( -140p + 9,000) + 16, 000
Now, expand the bracket, we get;
Expense function = - 280p + 18, 000 + 16, 000
collect and add like terms
Expense function = - 280p + 34, 000
If p = $10. 00
Then,
Demand function is q = -140(10) + 9,000
expand the bracket
q = - 1400 + 9, 000
q = 7, 600
Substitute q in expense function
E = 2.00q + 16,000
E = 2. 00(7600) + 16, 000
E = $31, 200
Hence, the expense function is - 280p + 34, 000
Learn more about functions here:
https://brainly.com/question/25638609
#SPJ1
A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
Using the trigonometry ratio, he angle of elevation of the ramp to the nearest degree is 11°.
In the given question,
A ramp goes from a doorway of a building to the ground.
The end of the ramp connected to the doorway is 1 foot above the ground.
The distance along the ramp to the building is 5 feet.
We have to find the angle of elevation of the ramp to the nearest degree.
The distance is 5 feet.
The height is 1 foot.
To find the angle of elevation we used the trigonometry ratio.
According the trigonometry ratio, we know that tangent is the ratio between height and distance.
We can write it as
tan A=height/distance
Now putting the value
tan A=1/5
tan A=0.2
So A = arctan(0.2)
A = 11.30°
A ≈ 11°
Hence, the angle of elevation of the ramp to the nearest degree is 11°.
To learn more about trigonometry ratio link is here
brainly.com/question/28820002
#SPJ1
Suppose that 14 inches of wire costs 70 cents. At the same rate, how many inches of wire can be bought for 50 cents?
Answer:
10 inches
Step-by-step explanation:
What this question is asking you to do is set up a ratio. So all you do is 14/70 = x/50 and solve for x.
Answer:
14inches = 70cents
X inches = 50cents
70x = 50×14
70x = 700
X = 10inches
find the missing angle measures
a=b
b=(b+16)
c=(2b)
Answer:
a = 41°
b = 57°
c = 82°
Step-by-step explanation:
all angles in a triangle must add up to equal 180°
so 4b + 16 = 180180 - 16 = 4b164 = 4b164 / 4 = 41b = 41°therefore a = 41°, b = (41 + 16) --> 57°, and c = 2(41) = 82°Only 9 people can be in a roller coaster cart. How many people can fit in nine train carts
Answer:
81 people
MARK AS BRAINLIEST
There are 90 new houses being built in a neighborhood.last month, 1/5 of them were sold. this month,1/3 of the remaining houses were sold. How many houses were left to be sold?
Step-by-step explanation:
1:
1/5 of 90 = 18 hours which are sold.Means are 72 houses left.
2.
1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold
Graph a line with a slope of 1/5 and passes through the point (-2, 2).
The equation of line in slope intercept form
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = [tex]\frac{1}{5}[/tex]
Point = (-2, 2)
Required equation of line =
[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]
The graph has been attached here.
To learn more about equation of line in slope intercept form, refer to the link-
brainly.com/question/25514153
#SPJ1
solve for x. "-8+x/4=-4" simplify your answer as much as possible
Answer:
48
Step-by-step explanation:
multiply by 4 to make x whole number
-32+x=16
+32 to isolate x
x=16+32
add for answer
x=48
(2/7 , −3) ; r = 6 standard form of circle
a) 50 students in a hostel had provisions for 60 days. (i) How long would the provisions last for 1 student? (ii) How long would the provisions last for 40 students?
Answer:0.8
Step-by-step explanation:
0.8 can be used for 1 student and 40. :)
The values are;
i, For 1 student, it would take = 1 1/5 days
ii. For 40 students, 48 days
How to determine the daysFirst, we need to know that proportion is an equation made equal to another.
From the information given, we have that;
50 students in a hostel had provisions for 60 days.
This is represented as;
50 students = 60 days
Then, we get that;
i, If 50 students = 60 days
1 students = x days
cross multiply the values
x = 60/50
x = 1 1/5 days
ii. If 50 students = 60 days
40 students = x days
x = 60(40)/50
divide the values
x = 48 days
Learn about proportion at: https://brainly.com/question/1781657
#SPJ2
Levine Labs used 50,000 ounces of specimen adhesive during the year. The direct materials standard allows 1.50 ounces of adhesive at a price of $0.40 per ounce for each pathology test. The direct materials quantity variance was $880 Favorable.
How many pathology tests did Levine Labs complete during the year?
(Round per unit value to 2 decimal places, e.g. 15.25 and final answer to O decimal places, e.g. 125.)
Pathology tests ____?
The number of pathology tests that were completed during the year by Levine Labs are 34,800 tests.
What is the calculation showing the above answer?Note that Material quantity variation - Material quantity variation describes the cost difference caused by variations in the actual material used and the standard material to be utilized.
Material quantity Variance =
(Actual material used- Standard material used) x Standard cost
(50000-no of test x 1.5) x 0.4 = -880
-2200 = 50000-(No of test*1.5)
No of test x 1.5 = 52,200
No of test = 52,200/1.5
No of test = 34,800
Learn more about pathology tests:
https://brainly.com/question/14993214
#SPJ1
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).
Temperature: Days:
50-59 5
60-69 309
70-79 1496
80-89 1521
90-99 533
100-109 6
(a) Approximate the mean and standard deviation for temperature.
B) Use the frequency histogram of the data to verify that distribution is bell shaped. Yes or No
C) According to the Empirical rule, 95% of the days in the month will be between what two temperatures?
Regarding the data-set of the temperatures, it is found that:
a) The mean and the standard deviation are given as follows:
Mean: 80.41Standard deviation: 8.33.b) The histogram is bell shaped.
c) 95% of the days will be between 63.75 ºF and 97.07 ºF.
How to obtain the mean and the standard deviation?The first step towards obtaining the mean and the standard deviation is obtaining the relative frequencies, which are the absolute frequencies divided by the number of observations.
The number of observations is:
5 + 309 + 1496 + 1521 + 533 + 6 = 3870.
Considering the midpoint of each interval, the following distribution is built:
P(X = 54.5) = 5/3870 = 0.0013.P(X = 64.5) = 309/3870 = 0.0798.P(X = 74.5) = 1496/3870 = 0.3866.P(X = 84.5) = 1521/3870 = 0.3930.P(X = 94.5) = 533/3870 = 0.1377.P(X = 104.5) = 6/3870 = 0.0016.The mean is given by the sum of each value multiplied by it's relative frequency, hence:
E(X) = 54.5 x 0.0013 + 64.5 x 0.0798 + 74.5 x 0.3866 + 84.5 x 0.3930 + 94.5 x 0.1377 + 104.5 x 0.0016 = 80.41.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, multiplied by their relative frequencies, as follows:
S(X) = sqrt((54.5-80.41)² x 0.0013 + (64.5-80.41)² x 0.0798 + (74.5-80.41)² x 0.3866 + (84.5-80.41)² x 0.3930 + (94.5-80.41)² x 0.1377 + (104.5-80.41)² x 0.0016) = 8.33.
From the histogram, most values are around the mean, with a small percentage of around 0.3% around the bounds, accordingly with the Empirical Rule, hence the distribution is normal.
By the Empirical Rule, a percentage of 95% of the observations is within two standard deviations of the mean, hence:
80.41 - 2 x 8.33 = 63.75.80.41 + 2 x 8.33 = 97.07.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
#SPJ1
1. What is the missing number 56/7=?-5
Answer:
13
Step-by-step explanation:
56/7 = 8
13 - 5 = 8
15/7 = 13 - 5
The missing number in the expression is 13.
We have,
To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.
Unknown value = x
Starting with the equation 56 / 7 = x - 5, simplify the left side:
56 / 7 = x - 5
8 = x - 5
x = 8 + 5
x = 13
Thus,
The missing number in the expression is 13.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ6
If a circle has an Area of 84.9056, find the radius and the circumference of the circle.
(Use π=3.14 and do not round.)
Radius =
Circumference =
Answer: Radius is estimated to = 5.2
Circumference is estimated to = 32.66
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
The proportions of the total rooms that were occupied each year are:
The current year is 84%.The previous year is 81%.What is the proportion?Proportion is the fractional value of a variable when compared to the whole.
Proportions show the ratio or relative relationship between two or more values set as equal.
Like ratios, proportions are depicted in fractions, decimals, or percentages to show how two values compare.
Current Year Previous Year
Occupied Rooms 1,512 1,458
Total Rooms 1,800 1,800
Proportion of occupied rooms = 84% 81%
(1,512/1,800 x 100) (1,458/1,800 x 100)
Thus, on average, room occupancy for the two years is 82.5%, and proportionately for each year, it is 84% for the current year, while the previous year recorded 81%.
Learn more about proportions at https://brainly.com/question/1496357
#SPJ1
Question Completion:What proportion of the total rooms were occupied each year?
6x-5=6x-5 pls help fast
Answer:
0=0
Step-by-step explanation:
Answer: Infinite Solutions
Step-by-step explanation:
Hello! Let's solve this equation.
[tex]\textbf{First, add 5 to both sides.}[/tex][tex]\sf{6x-5=6x-5}[/tex]
↓
[tex]\sf{6x=6x-5+5}[/tex]
↓
[tex]\sf{6x=6x}[/tex]
[tex]\textbf{Next, subtract 6x from both sides.}[/tex][tex]\sf{6x-6x}[/tex]
↓
[tex]\sf{0}[/tex]
[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3000 for 3 years at %4 compounded semiannually.
The amount in the account is ____.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The amount in the account is $3499. 2
How to determine the compound interestThe formula for determining compound interest is given as;
A = P ( 1 + r/ n) ^nt
Given that;
A is the final amountP is the principal amountr is the ratet is the time taken n is the number of times interest applied per periodSubstitute the values into the formula, we have;
A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)
Find the exponential value
A = $3000 ( 1 + 0. 04 / 0. 5) ^2
A = $3000( 1+ 0. 08)^2
Expand the bracket, we get;
A = $3000 (1. 08)^2
A = $3000(1. 17)
multiply through
A = $3499. 2
Hence, the value is $3499. 2
Learn more about compound interest here:
https://brainly.com/question/24924853
#SPJ1
At one time the thickness of different gauges of stainless
steel were given in fractions of an inch. Today, these
thicknesses are listed as decimal numbers. Convert each of
the following fractional thicknesses to decimal form.
A fraction can be converted into decimal form by dividing it. The answer to these parts are in main body.
What is a decimal?
When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number.
Main Body:
a) 15/32 = 0.4688
b) 13/64 = 0.2031
c) 9/16 = 0.5625
d) 5/8 = 0.625
e) 7/80 = 0.0875
f) 29/1280 = 0.0227
to learn more about decimals click on the link below;
https://brainly.com/question/1827193
#SPJ13
1. Write and solve an equation for the following statement: Eight less than one-third of a number,
Answer: (1/3)x - 8
Step-by-step explanation:
one - third means 1/3
one - third of a number means (1/3)x
( x being the number )
Eight less means -8
Eight less than 1/3 of an number is (1/3)x - 8
5.
A car service charges $2.40 for driving 1 mile. How much does the company charge for
driving 12.45 miles?
) (
$14.85
$24.85
$27.48
$29.88
Show Your Work
Answer:
Step-by-step explanation:
$2.40 12.45 mi
___ * ___ = ? ;
1 mi. 1
The units of miles— "mi" —cancel out to "1" ;
since: " mi/ mi = 1 "
and we have:
$2.40 * 12.45 = ? ;
= $29. 88 ; {using a calculator};
⇒ which corresponds to: Answer choice: [D]: $29.88 .
_____
Hope this is helpful!
Best wishes!
_____
Choose which property of equality is demonstrated.
a. AB = AB
In Ty’s English class 70% of the students completed and essay by the due date there are 30 students in Ty’s English class how many completed the essay by the duet date?
21 students completed the essay by due date
What is unitary method ?In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple. How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used.
Calculation30 ----------> whole
30 ----------> 100 %
0.3 -----------> 1%
multiplying both sides by 70
21 ----------> 70 %
therefore 21 students completed the essay by due date .
learn more about unitary method here :
brainly.com/question/22056199
#SPJ13
Approximate the following square root to the nearest integer.
√10~