Step-by-step explanation:
= 40 + [ 3 { 18 ÷ ( 9 - 3 ) - 11 - 9 } + 4 ]
= 40 + [ 3 { 18 ÷ 6 - 11 - 9 } + 4
= 40 + [ 3 { 3 - 20 } + 4
= 40 + [ 3 {- 17 } + 4
= 40 + ( - 51 ) + 4
= 40 + 4 - 51
= 44 - 51
= - 7
[tex]...[/tex]
☘☘☘....
Answer:
[tex] \sf \large \: - 7[/tex]
Step-by-step explanation:
40+3(18/9−3−11−9)+4
=40+3(18/6−11−9)+4
=40+3(3−11−9)+4
=40+3(−8−9)+4
=40+(3)(−17)+4
=40+−51+4
=40+−47
=−7
The sum of the first five terms of an arithmetic sequence is 35. The sum of the next five terms is 85. Determine the first term and the common difference of the sequence.
Answer:
The first term is 3 and the common difference is 2
Step-by-step explanation:
The formula of the sum of the nth term of the arithmetic sequence is
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex], where
a is the first termd is the common differencen is the position of the term∵ The sum of the first five terms of an arithmetic sequence is 35
∴ [tex]S_{5}[/tex] = 35
→ Substitute The values of n and S in the rule above
∵ 35 = [tex]\frac{5}{2}[2a+(5-1)d][/tex]
∴ 35 = [tex]\frac{5}{2}[2a+4d][/tex]
→ Simplify the right side
∴ 35 = 5a + 10d
→ Switch the two sides
∴ 5a + 10d = 35 ⇒ (1)
∵ The sum of the next five terms is 85
→ To find the sum of the first 10 terms add 85 to [tex]S_{5}[/tex]
∴ [tex]S_{10}[/tex] = 35 + 85 = 120
→ Substitute The values of n and S in the rule above
∵ 120 = [tex]\frac{10}{2}[2a+(10-1)d][/tex]
∴ 120 = 5[2a + 9d]
→ Simplify the right side
∴ 120 = 10a + 45d
→ Switch the two sides
∴ 10a + 45d = 120 ⇒ (2)
Now we have a system of equations to solve it and find a and d
→ Multiply equation (1) by -2
∵ -2(5a) + -2(10d) = -2(35)
∴ -10a + -20d = -70 ⇒ (3)
→ Add equations (2) and (3)
∵ (10a + -10a) + (45d + -20d) = (120 + -70)
∴ 25d = 50
→ Divide both sides by 25 to find d
∴ d = 2
→ To find a substitute d in equation (1) by 2
∵ 5a + 10(2) = 35
∴ 5a + 20 = 35
→ Subtract 20 from both sides
∵ 5a + 20 - 20 = 35 - 20
∴ 5a = 15
→ Divide both sides by 5
∴ a = 3
∴ The first term is 3 and the common difference is 2
the principal of a high school wants to gather opinions from the parents of students at his school. he starts with the 2nd name in the parents teacher association (pta) phone handbook and then selects every 5th name in the directory. the 2nd, 7th, 12th, … names in the directory are chosen for his sample. this is an example of a/an sample.
This example is an part of systematic sampling.
What are the advantages and disadvantages of systematic sampling ?Simple to Use and Understand.A sense of process and control.Clustered Selection is no longer used.Low risk componentassumes it is possible to estimate the population size.Natural Degree of Randomness is required.Data Manipulation Risk is Greater.
Disadvantage
A population must be closely approximated for this procedure to work.Some populations are able to recognize the sample pattern.A little likelihood of selection is produced.There is a significant risk of data manipulation.In comparison to random sample, systematic sampling is less random.To learn more about systematic sampling, visit
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C
15 mm
8 mm
Pythagorean theorem
What is the slope of the line that passes through points (6, − 2) and (21, 3) ?
Answer: __________
Answer:
[tex]m=\frac{1}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (6, -2)
Point (21, 3)
Step 2: Find slope m
Substitute: [tex]m=\frac{3+2}{21-6}[/tex]Add/Subtract: [tex]m=\frac{5}{15}[/tex]Simplify: [tex]m=\frac{1}{3}[/tex]Solve the following absolute value equation'
2|x+3|-2=0
A(-2,-4)
B(4,2)
C(-3)
D(1,-7)
Answer: A(-2,-4)
Explanation:
2|x+3|-2 = 0
2|(-2)+3|-2 = 0
2|(-4)+3|-2 = 0
The slide at a playground
has a height of 22 feet. The
distance between the foot
of the ladder and the end of
the slide is 10 feet. What is
the length of the slide?
Round to the nearest tenth.
Answer:
c = 24.17 feet
Step-by-step explanation:
Right Triangles
A right triangle is a special triangle that has an interior angle of 90°.
In right triangles, Pythagora's Theorem is satisfied:
[tex]c^2=a^2+b^2[/tex]
Where c is the hypotenuse (longest side) of the triangle, and a and b are the legs or the smaller sides.
The slide can be thought of as a right triangle whose hypotenuse is the slide itself and the legs are the height of the ladder and distance between the foot of the ladder and the end of the slide.
So we have:
[tex]c^2=22^2+10^2[/tex]
[tex]c^2=484+100=584[/tex]
[tex]c=\sqrt{584}[/tex]
c = 24.17 feet
find the slope and y-intercept of the graph of the linear equation
y=-5x+2
Answer:
the y-intercept is 2/5 and the slope is -5
Step-by-step explanation:
I need help please!!!
Answer:(y=2x+2
Step-by-step explanation:
Kate and Nora each have a sum of money. The ratio of the amount of money Kate has to that of Nora is 3 : 5. After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9. Find the sum of money Kate had initially.
Given:
The ratio of the amount of money Kate has to that of Nora is 3 : 5.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
To find:
The sum of money Kate had initially.
Solution:
Let the initial amount of money Kate and Nora have are 3x and 5x respectively.
After Nora gives $150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes 7 : 9.
The amount of Kate = 3x+150
The amount of Nora = 5x-150
Now,
[tex]\dfrac{3x+150}{5x-150}=\dfrac{7}{9}[/tex]
[tex]9(3x+150)=7(5x-150)[/tex]
[tex]27x+1350=35x-1050[/tex]
[tex]1350+1050=35x-27x[/tex]
[tex]2400=8x[/tex]
Divide both sides by 8.
[tex]300=x[/tex]
Putting x=300 in 3x, to get the amount of money Kate has initially.
[tex]3(300)=900[/tex]
Therefore, the Kate initially had $900.
how much more time in hours did Allen spend Listening to music than playing tenis
f.2.88 hours
g.0.48 hours
h.2.40 hours
j.0.12 hours
Answer:
She spent 48 more min listening to music
Your answer is g 0.48 hours
Step-by-step explanation:
I hope this helps
Christine makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours?
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!
Michelle ordered 200 T-shirts to sell at the school carnival. She paid $2.80 per shirt, plus 5% of the total order for shipping. When she sells each T-shirt at the carnival, she adds a 150% markup to the total price she paid for the shirt (including the cost of shipping). What is the selling price of each T-shirt?
A. $4.27 per shirt
B. $4.41 per shirt
C. $4.20 per shirt
D. $4.11 per shirt
Answer: B, $4.41 per shirt
Step-by-step explanation:
To figure this out you want to first take the 200 shirts and multiply them by the cost of $2.80. This gives you a total of $560, without tax. The tax is 5%, so you want to take 560 and multiply it by .05 to find the amount of tax. This leaves you with $28 of taxes. Add that onto the already cost of $560, and it gives you a grand total of $588. She wants to sell the shirts with a 150% markup, so all you do is first find what Michelle really paid for each shirt with tax. Take the total cost of 588 and divide it by the number of total shirts which is 200. 588/200=$2.94 per shirt that Michelle paid. Times that by 1.5% and you get $4.41 per shirt that Michelle is selling.
You decide to put a new stone siding on the rectangular side of your
house, which measures 8 by 15 feet. If stone costs $3 per square foot,
what is the total cost of stone?
The graph of y = f(x) is the solid black graph below. Which function represents the dotted graph?
Answer:
y = -f(x - 5)
Step-by-step explanation:
the function of the dotted graph is f(x) shifted (or translated) 5 units to the right and then reflected across the x-axis.
shifting it to the right is happening by reducing every x value by 5 (so that we get for x the functional value of x-5).
and reflecting it across the x-axis simply means to flip the sign. everything that was originally above the x-axis is now with the same distance below the x-axis (and vice versa).
therefore, the new
y = -f(x - 5)
Select the correct answer.
Mrs. Jameson's math test scores are represented by the following data.
Which of the following lists the lower quartile, median, and upper quartile (in that order)?
O 55,78,100
O 67,78,92
O 92,78,67
O 67,78,100
Answer:
i'm pretty sure it's 67,78,92
Step-by-step explanation:
Hope this helps!
The correct answer is option B which is the lower quartile, median, and upper quartile are 67,78,92 respectively.
What is a box plot?A rectangle is created to represent the second and third quartiles, normally with a vertical line inside to indicate the median value, in a simple way of presenting statistical data on a plot.
As we can see in the given image the lower vertical line is lying at the point of 67 the middle line is lying at 78 and the higher vertical line is lying at 92.
Therefore the correct answer is option B which is the lower quartile, median, and upper quartile are 67,78,92 respectively.
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5. The two figures are congruent.
a. Label the points A, B and C that correspond to A, B, and C in the figure on
the right.
C
B
b. If segment AB measures 2 cm, how long is segment A' B'? Explain.
c. The point D is shown in addition to A and C. How can you find the point D' that
corresponds to D? Explain your reasoning.
Answer:
check image for answers
Step-by-step explanation:
Hope this is not to late. Have a good day!
Please help! I’ll mark brainlist and 5 stars!
(You have to see which one is right for the sentence provided, and which ones are false out of A-D)
A. The equation of the line is y = 1/2x
B. Sasha can make 60 gift bags in 2 hours.
C. The constant of proportionality is l = 1/2
D. Sasha can make 2 bags per minute.
Answer:
D
Step-by-step explanation:
The reason D is false is because it states that Sasha can make 2 bags per minute while she cant make 2 bags per minute. She can make half a bag per minute. D is wrong 100%
Answer:
Step-by-step explanation:
Distance covered = speed × time.
Sasha runs at a constant speed of 3.8 meters per second for 1/2 hour.
This means distance covered while running would be
3.8 × 1/2 = 1.9 meters
Then she walks at a constant rate of 1.5 meters per second for 1/2 hour. This means distance covered while walking would be
1.5 × 1/2 = 0.75 meters
Total distance that Sasha covered while running and walking in 60 minutes would be
1.9 + 0.75 = 2.65 meters
Step-by-step explanation:
If a cylindrical grain silo has height of 35 feet and a volume of 2747.50 ft?, what would the length of its radius be?
Answer:
784.39
Step-by-step explanation:
Cant really explain how I did it because I tend to confuse ppl.
Which best describes the effect on the x-intercept of the graph of y=34x−3 if the slope is changed to −34
The x-intercept remains the same and the new line is translated upwards
The x-intercept becomes negative and the new line is parallel to the original line
The x-intercept remains the same and the new line is translated downward
The x-intercept becomes negative and the new line intersects the original line
Answer:
The last option: The x-intercept becomes negative and the new line intersects the original line.
Step-by-step explanation:
Remember that when finding the x-intercept you set y to 0.
Let's compare the two equations when we solve for x:
0=34x-3 0=-34x-3
1. Add 3 to both sides of the equations
3=34x 3=-34x
2. Divide the coefficients
[tex]\frac{3}{34}[/tex]=x [tex]\frac{3}{-34}[/tex]=x
We know that the new slope does not remain the same as stated in the first and third options. In order for two lines to be parallel, the slopes must be exactly the same, so the second option is incorrect. Therefore, the last option is correct.
Answer:
Step-by-step explanation:
⊕ The x-intercept becomes negative and the new line intersects the original line { at (0, - 3) }
What is the area of a triangle whose base is 10 in and height is 5 in
Barbara bought a piece of rope that was 6 3/4 meters long. She cut the rope into 6 equal pieces. How long is each piece of rope?
Answer:
1 1/8
Step-by-step explanation:
Make this an improper fraction for simplicity: 27/4
now divide into six portions: (27/4)/6 = (27/6)/4 = 27/24 = 1 3/24 = 1 1/8
To complete bookshelves, a? At your store needs to purchase vertical brackets to attach to the wall. The customer wants to shelving to be 9 feet high and 10 feet long. The wall brackets come in 48 inches and 60 inch sections the 48 inch suction cost 1295 to 60 inch sections cost 1695 the bracket should be 1 foot from each And add no more than 24 inches apart. What will the total cost of the brackets before tax
Answer:
the total cost of the brackets before tax is $89.7
Step-by-step explanation:
The computation of the total cost of the bracket before tax is as follows
Given that
height = 9 feet
length = 10 feet
wall brackets:
48-in costing $12.95
60-in costing $16.95
The distance of brackets from ends is 1 foot
The maximum distance between brackets is 24 inches
Now based on the above information
The brackets are
= 48 ÷ 12
= 4 feet
And
= 60 ÷ 12
= 5 feet
The length of the shelf is 60 inch
Now the 1 could be deducted from each side
= 60 - 2
= 58 in
Now Divide it by 24 inches
= 58 ÷ 24
= 2.41 ~ 3
Finally, The total cost is
= ($12.95 + $16.95) × 3
= $89.7
Hence, the total cost of the brackets before tax is $89.7
Which statement describes a pattern in the shaded parts of the multiplication table?
A pattern in the shaded parts of the multiplication table is suitable for option b.(we multiply a number times itself to get each shaded number.)
Suppose we can use, option b,
We multiply a number times itself to get each shaded number,
Shaded parts of the multiplication table is ⇒ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
We can write,
[tex]x^{2}[/tex] = x * x
Example:
1 = 1 * 1 = 1
4 = 2 * 2 = [tex]2^{2}[/tex]
9 = 3 * 3 = [tex]3^{2}[/tex]
16 = 4 * 4 = [tex]4^{2}[/tex]
25 = 5 * 5 = [tex]5^{2}[/tex]
36 = 6 * 6 = [tex]6^{2}[/tex]
49 = 7 * 7 = [tex]7^{2}[/tex]
64 = 8 * 8 = [tex]8^{2}[/tex]
81 = 9 * 9 = [tex]9^{2}[/tex]
100 = 10 * 10 = [tex]10^{2}[/tex]
Hence,
1 = [tex]1^{2}[/tex]
4 = [tex]2^{2}[/tex]
9 = [tex]3^{2}[/tex]
16 = [tex]4^{2}[/tex]
25 = [tex]5^{2}[/tex]
36 = [tex]6^{2}[/tex]
49 = [tex]7^{2}[/tex]
64 = [tex]8^{2}[/tex]
81 = [tex]9^{2}[/tex]
100 = [tex]10^{2}[/tex]
Therefore,
We multiply a number times itself to get each shaded number statement is suitable for a pattern in the shaded parts of the multiplication table.
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Need help :((
plss help i took a screenshot so you can see
Answer: 5:4
Step-by-step explanation: you divide them i believe :)
Answer:
5:9
Step-by-step explanation:
Well it says the ratio to the blueberry muffins to all muffins so add together 12+15 which is 27 then compare the ratios in simplest form so 15:27 in simplified form is 5:9
Which situation is best represented by the following equation?
45w+123.95=753.95
A.Erica paid $753.95 for dance classes. She paid $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w,the number of weeks Erica was enrolled in dance classes?
B.Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
C.Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
D.Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?
Answer:
The correct answers is B.
Step-by-step explanation:
If you take a number multiply by 7 then takeaway 1,You get the same as if you took the number multiply by 5 then takeaway 8. What is the number?
Answer:
x = -3.5
Step-by-step explanation:
First we create the equation.
Let x = the unknown number
7x-1 = 5x - 8
Add 8 to both sides
7x + 7 = 5x
Subtract 7x
7 = -2x
Divide by 2
-7/2 = x
-3.5 = x
What is the area of a circle with a 17cm diameter?
Lauren saved $25 a month for 2 years. She spent 75% of her savings on a TV. How much money does Lauren have left?
Answer
$150
Step-by-step explanation:
Since there are 12 months in year, you multiply 25 times 24 to get 600. 75% of 600 is 450, so then you do 600-450. The answer to that is 150.
Hope this helped!
whats 4 time 100 yeah im not
100+100+100+100=400
The answer is 400.
Answer:
400
100+100+100+100
Step-by-step explanation:
What is f(0) if f(t) = t^2 – 2t – 2?
Answer:
-2
Step-by-step explanation:
f(t) = t^2 – 2t – 2
To find f(0), replace t with 0 in the expression and evaluate the expression.
f(0) = 0^2 – 2(0) – 2
f(0) = -2
0 = t
We know this because 0 replaced t in the parenthesis next to F !
The question is just asking you to plug in 0 where ever t is!
Let's do it
[tex]f(0) = 0^{2} - 2(0) - 2[/tex]
solve
[tex]0^{2} = 0 \\2 ( 0 ) = 0[/tex]
so, this is what we have left!
[tex]f(0) = 0 - 0 - 2[/tex]
We have our answer!
[tex]f (0) = -2[/tex]