Answer:
The sum of all the even integers between 99 and 301 is 20200
Step-by-step explanation:
For the sum of all the even integers between 99 and 301, this can be calculated using the formula for Sum of n terms in an Arithmetic Progression (AP)
Sum of n terms in an AP [tex]S_{n}[/tex]= [tex]\frac{n }{2}[ 2a + (n - 1)d][/tex]
Where [tex]n[/tex] is the number of terms
[tex]a[/tex] is the first term
and [tex]d[/tex] is the common difference
The AP for the sum of all the even integers between 99 and 301 will look like
100 + 102 + 104 + ... + 300
[tex]a[/tex] = 100
[tex]d[/tex] can be calculated by taking the difference of the first two terms or any two consecutive terms of the AP
Hence, [tex]d[/tex] = 102 - 100 = 2
[tex]n[/tex] can be determined from the formula used to calculate the Last term of an AP
[tex]l = a + (n - 1)d[/tex]
Where [tex]l[/tex] is the last term
In the AP, the last term, [tex]l[/tex] = 300
Then
[tex]300 = 100 + (n - 1)2\\300 - 100 = (n - 1)2\\200 = (n - 1) 2\\(n - 1) = 200 / 2\\n - 1 = 100\\n = 100 + 1\\n = 101[/tex]
Hence, there are 101 terms in the AP
Now, to determine the sum
[tex]S_{n}[/tex]= [tex]\frac{n }{2}[ 2a + (n - 1)d][/tex]
[tex]S_{n} =\frac{101}{2}[ 2(100) + (101 - 1)2]\\ S_{n}=\frac{101}{2}[ 200 + (100)2]\\ S_{n}=\frac{101}{2}[ 200 + 200]\\S_{n}=\frac{101}{2}[ 400]\\S_{n} = 20200[/tex]
Hence, the sum of all the even integers between 99 and 301 is 20200
Use h(x) = x2 +4 to find x when h(x) = 29.
Answer:
In this question the value of x is given 29 so put it in the equation to get answer
[tex]h(x) = {x}^{2} + 4[/tex]
put the value of x = 29 in the above equation
[tex]h(x) = {29}^{2} + 4[/tex]
so after solving this equation we get our answer
[tex]h(x)= 841 + 4[/tex]
[tex]h(x) = 845[/tex]
Hope it helps u mate
if u like leave a thank
Answer:
the variable x=12.5
Step-by-step explanation:
so first you will insert 29 to the equation
29= x2+4
now you subtract 4 from 29
29-4= 25
since you are multiplying you have to do the opposite operation which would be division so now divide 25 by 2
25/2
now insert your answer
h(12.5)=(12.5)2+4
h would be considered 2.32
what is the answer to -19+66
Answer: Adding a negative is the same as subtracting, so we will subtract 19 from 66.
66 - 19 = 47
The answer to -19 + 66 is equal to 47.
If $(ax+b)(2x+3)=20x^2+44x+21$, where $a$ and $b$ are two distinct integers, what is the value of the sum $a+b$?
Answer: 17
Step-by-step explanation:
Given: [tex](ax+b)(2x+3)=20x^2+44x+21[/tex], where a and b are two distinct integers.
First simplify left hand side as
[tex](ax+b)(2x+3)=ax\cdot \:2x+ax\cdot \:3+b\cdot \:2x+b\cdot \:3\\\\=2axx+3ax+2bx+3b\\\\=2ax^2+(3a+2b)x+3b[/tex]
Then comparing left side and right side
[tex]2ax^2+(3a+2b)x+3b=20x^2+44x+21[/tex]
we get 2a = 20 (coefficient of [tex]x^2[/tex]) , and 3b = 21 (constant term)
⇒ a= 10 and b= 7
Then, a+b= 10+7=17
Hence, the value of sum a+b is 17.
please help me on this geometry!!!
Answer:
Solution : 29
Step-by-step explanation:
As this is an equilateral triangle all sides present are congruent.
3x + 8 = 5x - 6 = 2x + 15
3x + 8 = 5x - 6
- 2x = - 14,
x = 7
And hence one side length will be say 3(7) + 8 = 21 + 8 = 29 units. We can double check this solution by substituting x for other side lengths. Remember that all the side length have an equal measure.
5(7) - 6 = 35 - 6 = 29 ✓
2(7) + 15 = 14 + 15 = 29 ✓
what does n equal? 2=-9n+22-n
Answer:
n =2
Step-by-step explanation:
2=-9n+22-n
2 = -10n +22
-20 = -10n
n = 2
Step-by-step explanation:
Grouping like terms
9n+n=22-2
10n=20
Dividing through by 10
n=2
please help I will mark you BRANLEST
Help please, -16-4g=6g-6g?
Answer:
the answer is -4
Step-by-step explanation:
-16-4g=6g-6g
+4 +4
you add the -4g to both sides by changeing it to positive
then you have -16=6g-2g
then you go to the right side of the equation and solve, 6-2 is 4 then you have
-16=4g then you divide on both sides
-16 divided by 4 is
-4
Answer:
[tex]\Huge \boxed{g=-4}[/tex]
Step-by-step explanation:
[tex]-16-4g=6g-6g[/tex]
Combining like terms.
[tex]-16-4g=0[/tex]
Adding 4g to both sides.
[tex]-16=4g[/tex]
Dividing both sides by 4.
[tex]-4=g[/tex]
the volume of this cube is 8 cubic inches. what is the surface area of this cube
Answer:
Step-by-step explanation:
find the height, width, and length.
multiply them
V=lwh
or
V=Bh
B=lw
Carmen made 80 ounces of peach jam and 96 ounces of strawberry jam. If each jam Will hold 8 ounces of jam how many jars will she need to hold off jam?
Answer:
80+96
= 176 total ounces of jam
176 ÷ 8
22 total jars
Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales. She sold $600 in clothing on Saturday and $1200 in clothing on Sunday. How much did she earn over the two days?
Answer: $ 532
Step-by-step explanation:
Given: Ramona works in a clothing store where she earns a base salary of $140 per day plus 14% of her daily sales.
She sold $600 in clothing on Saturday and $1200 in clothing on Sunday.
To find : Earning in two days.
Total sales she did in 2 days = $600+$1200 = $1800
Then, her total earning for 2 days = 2 x( Base salary)+ 14% of (Total sales)
= 2 x ($140) + (0.14) ($1800)
= $(280+252)
= $ 532
Hence, she earned $ 532 over the 2 days.
Answer:
$532
Step-by-step explanation:
Ramona worked for two days. So she would have already earned $280.
And she also earns 14% of $600 from the first day, and 14% of 1200.
14/100 * 600/1 = 8400/100 = $84
14/100 * 1200/1 = 16800/100 = $168
$280 + $84 + 168 = $532
Altogether, Ramona earned $532 in the total of two days! Wow that's more money then I get per month lol.
Hope this helps :D
- Anna
I need help answering this question
Answer:
55
Step-by-step explanation:
JL = JK + KL
84 = 3x+5 + 6x+7
Combine like terms
84 = 9x +12
Subtract 12 from each side
84-12 = 9x+12-12
72 = 9x
Divide by 9
72/9 = 9x/9
8 =x
We want KL
KL = 6x+7
6*8 +7
48+7
55
Use the key features of the polynomial f(x) = 6x^4 + 4x^3 - 5x^2 -2x + 1 to describe its end behavior. A. The left side continues up, and the right side continues up. B. The left side continues down, and the right side continues down. C. The left side continues up, and the right side continues down. D. The left side continues down, and the right side continues up.
Answer:
A. The left side continues up, and the right side continues up.
Step-by-step explanation:
f(x) = 6x^4 + 4x^3 - 5x^2 -2x + 1
The highest power will describe the end behavior
f(x) = 6x^4
Let x = -∞
f(-∞) = 6 * (-∞)^4 = 6* ∞ = ∞
As x goes to -∞ f(x) goes to ∞
Let x = ∞
f(∞) = 6 * (∞)^4 = 6* ∞ = ∞
As x goes to ∞ f(x) goes to ∞
Apply
10. Fouster's Farms has 53 fruit trees on their land. Myrna's Farms has five
times as many fruit trees as Fouster's. A commercial farm has 500 fruit
trees. Which farm has the most fruit trees?
Answer:
myrna farm has 265 and the commercial farm 500
Step-by-step explanation:
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The farm that has the most fruit trees are commercial farm.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that Foster's Farms has 53 fruit trees on their land. Myrna's Farms has five times as many fruit trees as Foster's. Therefore, the number of trees on Myrna's farm is,
Number of trees on Myran's farm = 5 × Number of trees on Foster's farm
= 5 × 53
= 265 trees
Since the number of trees on Myran's farm and Foster's farm is 265 trees and 53 trees, respectively, while the number of trees on the commercial farm has 500 fruit trees.
Hence, The farm that has the most fruit trees are commercial farm.
Learn more about Multiplication here:
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Choose all of the statements that correctly define the geometric term. 1)Two rays joined at the same end point form an angle.2) Intersecting lines that form right angles are parallel lines 3) A continuous section of the circumference of a circle is a circular arc. 4)Lines that never intersect or cross each other perpendicular. 5)A circle is the locus of all points a fixed distance from a given center point.
Answer:
67
Step-by-step explanation:
Answer:
Statements 1, 3, and 5
1) Two rays joined at the same end point form an angle.
3) A continuous section of the circumference of a circle is a circular arc.
5) A circle is the locus of all points a fixed distance from a given center point.
Step-by-step explanation:
Statement 2 is false because it says that intersecting lines that form right angles are parallel lines. Actually, intersecting lines that form right angles are perpendicular lines.
Statement 4 is false because it says that lines that never intersect of cross each other are perpendicular. Actually, lines that never intersect or cross each other are parallel.
50+5w+20m what is the coefficient variable and constant in this expression
Answer:
Find the degree, leading term, and leading coefficient.
Polynomial Degree: 1
Leading Term: 20 m
Leading Coefficient: 20
Step-by-step explanation:
If 9 is p present of 17 then p is a number between
Answer:
40% and 60%
╰(*°▽°*)╯
Step-by-step explanation:
60% of 17 is 10.2 making 40% and 60% the closest choice to 9
So, the answer would be 40% and 60%
╰(*°▽°*)╯
Answer: p lies between 50% and 55%
Step-by-step explanation: if 9 is p percent of 17, then p is a number between what numbers
9 is p percent of 17
Lets make the equation for the given statement
9 = p percent times 17
p percent is p /100
Lets solve for p
multiply both sides by 100
Divide both sides by 17
p= 52.9
Hence we say that p lies between 50% and 55%
What does change and what does NOT change during a translation? *
Answer:
During a translation the location of a figure changes, but the orientation, area, and lengths between it's points do not.
Answer:
the size and the shape
Step-by-step explanation:
Find the volume of a box with a length of 5 cm, a width
of 5 cm, and a height of 10 cm.
Answer:
250 cm³
Step-by-step explanation:
The volume of a box will always be the value of multiplying its 3 dimensions. Since the dimensions of this box are 5, 5, and 10, the volume is:
[tex]5\cdot5\cdot10=250[/tex] cm³.
Hope this helped!
Answer:
250 cm^3
Step-by-step explanation:5x5x10
Which is the mode for the data set?
-1, 0, 3, 4, 3, 1
-0.5
0.3
2
-1
Answer:
3Step-by-step explanation:
-1 appears once
0 appears once
3 appears twice
4 appears once
1 appears once
Answer: -1
Step-by-step explanation: -1
occurs the most.
Find the limit. Please show all workings.
Answer:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}=2x-2[/tex]
Step-by-step explanation:
We want to find the limit:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}[/tex]
We can expand the numerator:
[tex]=\displaystyle \lim_{\Delta x \to 0} \frac{(x^2+2x\Delta x+\Delta x^2)+(-2x-2\Delta x)+1+(-x^2+2x-1)}{\Delta x}[/tex]
Simplify. Combine like terms:
[tex]\displaystyle \lim_{\Delta x\to 0} \frac{(x^2-x^2)+(-2x+2x)+(1-1)+(2x\Delta x+\Delta x^2-2\Delta x)}{y}[/tex]
The first three terms will cancel:
[tex]\displaystyle \lim_{\Delta x\to 0} \frac{2x\Delta x+\Delta x^2-2\Delta x}{\Delta x}[/tex]
Factor:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{\Delta x(2x+\Delta x-2)}{\Delta x}[/tex]
Cancel:
[tex]\displaystyle \lim_{\Delta x\to 0}2x+\Delta x-2[/tex]
Now, we can use direct substitution:
[tex]\displaystyle \begin{aligned} &\Rightarrow 2x+(0)-2\\ &=2x-2\end{aligned}[/tex]
Therefore:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}=2x-2[/tex]
Answer:
2x-2
Step-by-step explanation:
let d = delta x
lim as d goes to 0 ( ( x+d)^2 - 2(x+d) +1 - ( x^2 -2x+1))/d
Expand the term in side the parentheses
( ( x+d)^2 - 2(x+d) +1 - ( x^2 -2x+1))
x^2 +2dx +d^2 -2x-2d+1 - x^2 +2x -1
Combine like terms
2dx +d^2 -2d
Replace
lim as d goes to 0 ( 2dx +d^2 -2d)/d
Factor out a d
lim as d goes to 0 d( 2x +d -2)/d
Cancel the d in the numerator and denominator
lim as d goes to 0 ( 2x +d -2)
Take the limit of each term as d goes to zero
2x +0-2
2x-2
What is the cost in dollars for the nails to build a fence 125 meters long if it requires 30 nails per meter? Assume that 40 nails are sold per box at a cost of $0.75 per box.
Answer: $70.50
Step-by-step explanation:
30npm x 125m = 3750 nails total
3750/40 = 93.75, meaning you will need 94 boxes to complete the fence
94x0.75= $70.50
The cost in dollars for the nails to build a fence 125 meters long will be $70.31.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
A fence is 125 meters long if it requires 30 nails per meter. Then the total number of the nail will be
⇒ 125 x 30
⇒ 3750 nails
Assume that 40 nails are sold per box. Then the total number of boxes of nail will be
⇒ 3750 / 40
⇒ 93.75 boxes
The cost of $0.75 per box. Then the total cost of nails will be
⇒ 93.75 x $0.75
⇒ $70.31
Then the cost in dollars for the nails to build a fence 125 meters long will be $70.31.
More about the Algebra link is given below.
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On your first day of work you get 1 dollar on your second day you get 4 dollars on your third day you get 9 dollars on your fourth day you get 16 dollars.It continues for 30 days an then you receive a completion bonus of 500,000
Answer:
Step-by-step explanation:
How do you find a function for this story?
On your first day of work, you get $1. On your second day of work, you get $4. On your third day of work, you get $9. On your fourth day of work, you get $16. It continues this way for 30 days and then once you’ve completed the 30 days you receive a completion bonus of $500000.
No. of days Amount earned
1 1
2 4
3 9
4 16
. .
. .
. .
30 500,000
To find a function to the story
Let
No. of days = d
Amount earned = A
When,
d=1, A=1
d=2, A=4
d=3, A=9
d=4, A=16
It can be seen that amount earned is a square of the number of days
Therefore,
The function for the story is:
A=d^2
When d=30
A=30^2
=30*30
=900
Adding the total earnings for 30 days=$500,000
That is
1+4+9+16+25+36+49+64+81+100+121+144+169+196+225+256+289+324+361+400+441+484+529+576+625+676+729+784+841+900=500000
A recipe calls for 2 cups of sugar, 2 eggs, 3 cups of flour, and 5 cups of milk. What is the ratio of sugar to flour?
Answer:
2 cups of sugar:3 cups of flour
Step-by-step explanation:
Because there are 2 cups of sugar and 3 cups of flour used, you can represent this with a ratio - 2 cups sugar:3 cups flour.
Because 2:3 cannot be reduced (it is in its simplest form), this is the final answer.
If x = -12, y = -3; find xy?
Given that :-
x = -12 y = -3To Find :-
Value of xySolution :-
☆ When a negative digit is multiplied with negative digit then the result comes as positive digit .
→ x × y = (-12)(-3)
→ x.y = 36
So the answer is 36.
Answer:
36
Step-by-step explanation:
To find xy, multiply x and y
(-12)(-3) = 36
xy = 36
Which of the following choices will evaluate the expression a2 + b when a = 2 and b = 3?
A. 7
B. 10
C. 25
D. None of these choices are correct.
Work Shown:
Replace every 'a' with 2, and replace every b with 3
a^2+b = 2^2 + 3 = 4 + 3 = 7
The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are
Answer:
The expected frequencies for all categories are at least 5.
Step-by-step explanation:
The chi-square goodness of fit test is useful when we have one categorical variable from a population. The test is used to determine whether the data collected are consistent with a hypothesized distribution.
The conditions required to use the chi-square goodness of fit test are:
The sample collected should be a simple random sampleCategorical variable can only be testedThe expected frequencies for all categories or levels are at least 5.The degrees of freedom of this test is:
d = k - 1
Here,
k = number of categories.
Thus, the expected frequencies for all categories are at least 5.
Before her shopping spree, Lemon owned 11 shirts. Then she bought some more and now she owns 33 of them. What is the ratio of shirts before the purchase to the total number of shirts after the purchase
Answer:
So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3
Step-by-step explanation:
In this question we have to find the ratio of before and after so It will be written like this
Before : After
11: 33
Dividing both sides with 11
11/11:33/11
1: 3
So the ratio of shirts before the purchase to the total number of shirts after the purchase is 1:3
Which means that if we have total of 4 shirts then the number of shirts before the purchase were 1 and after the purchase were 4 meaning there are 3 new shirts in place for every single old shirt.
n + m - a = d, solve for m
Answer:
Hey there!
n+m-a=d
m+n=d+a
m=-n+d+a
m=a+d-n
Hope this helps :)
of the 60 questions, I got 80% right...How many questions did I get right?
Traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it take to drive 126 miles from San Diego to Malibu
65 miles per hour / 60 minutes per hour = 1.083 miles per minute.
126 miles/ 1.083 miles per minute = 116.03 minutes
Rounded to nearest whole number = 116 minutes.
Answer:
116 minutes
Step-by-step explanation:
speed = distance/time
speed * time = distance
time = distance/speed
time = 126 miles / 65 mph
time = 126/65 hours
time = 126/65 hours * (60 minutes)/(1 hour) = 116 minutes