Answer:
$5,824
Step-by-step explanation:
5,200*.04=208
208*3=624
5,200+624=5,824
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
Answer:
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
The oldest child in a family of four children is twice as old as the yougest. The two middle children are 12 and 16 years old. If the average age of the children is 15.25 , how old is the youngest child?
The age of the youngest child will be 11 years old.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The oldest child in a family of four children is twice as old as the youngest.
Let x be the age of the youngest child and y be the age of the oldest child. Then the equation is given as,
y = 2x ...1
The two middle children are 12 and 16 years old. If the average age of the children is 15.25. Then the equation is given as,
(x + 12 + 16 + y) / 4 = 15.25
x + y = 33 ...2
From equations 1 and 2, then we have
x + 2x = 33
3x = 33
x = 11
The age of the youngest child will be 11 years old.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Evaluate Sin^-1 sqrt2/2
Step-by-step explanation:
Let x = arcsin(√2/2).
We have sinx = √2/2, which is a basic trignometry identity. (sin45° = √2/2)
Since the range of arcsinx is [-90°, 90°] and 45° is within the range, the answer is 45° or π/4.
"Calculate the value of a in the triangle below." PLEASE HELP WILL GIVE BRAINLIEST
Using Pythagoras Theorem,
(12)^2+ (a)^2= (13)^2
144+a^2= 169
a^2= 169-144
a^2= 25
a= √25
a= 5mm
Hope it helps you.
SPORTS A coach uses a metric to determine the athletes that make the Varsity, Junior Varsity A, and Junior Varsity B teams. The total number of points possible on a skills test is 350. Athletes will make "Varsity" with at least 90% of the points. Athletes will make "Junior Varsity A" for 70-89% of the points. Athletes will make "Junior Varsity B" for 50-69% of the points. The table shows the number of points for each athlete that tried out.
Answer:
there is no picture. :)
Step-by-step explanation:
Answer:
Varsity = 12
Jr Varsity A = 10
Jr Varsity B = 11
Step-by-step explanation:
Varsity = at least 90% = 350 times 90% = 315
Anything 315-350
Jr Varsity A = 70-89%
350 times 70% = 245
350 times 89% = 311.5
Jr Varsity b = 50-69%
350 times 50% = 175
350 times 69% = 241.5
What is the volume of this figure?
16 cubic feet
216 cubic feet
36 cubic feet
108 cubic feet
Answer:
108 cubic feet
Step-by-step explanation:
Multipy Base, height, and width.=
Answer:
108 cubic feet
Step-by-step explanation:
Use the formula for finding the volume of a rectangular solid to solve the problem. V=lwh
I paid 7% tax on a vest. If the tax was $1.47, what was the cost of
the vest?
Answer:
21
Step-by-step explanation:
Answer:
cost of vest is $21.00
Step-by-step explanation:
set up and equation:
let x be cost of vest
0.07x=1.47
÷0.07 ÷0.07
x= 21
Which of the following options 70
How many solutions does
Y = 2x + 10
3y - 6x = 30
Show all work
A no solution
B one solution
C infinity solutions
Answer:
A no solution
Step-by-step explanation:
y = 2x + 10
3y - 6x = 30
3(2x+10) -6x =30
6x +30 -6x =30
6x -6x = 30-30
0=0
PLZ HELP ITS DUE TONIGHT
Because two pairs of angles are congruent, the triangles are similar by
the (select)
QR=
AA Criterion.
QR is similar to BC
Hope it helps.
Please help.
Of the 400 6th grade students at Aviara Oaks Middle School, the ratio of boys to girls is 2:3. Of the 360 students at Valley Middle School, the ratio of boys to girls is 3:5.
Which middle school has more boys attending their school?
How many girls attend AOMS?
How many girls attend VMS?
What is the ratio of girls attending Aviara Oaks Middle School to girls attending Valley Middle School?
Answer:
Step-by-step explanation:
Aviara Oaks Middle School:
Total student = 400
Boys : girls = 2:3
Boys = 2x , girls = 3x
2x + 3x = 400
5x = 400
x = 400/5
x = 80
Number of boys = 2x = 2*80 = 160
Number of girls = 3x = 3 *80 = 240
VMS:
Total student = 360
Boys : girls = 3 : 5
Number of boys = 3x
Number of girls = 5x
3x + 5x = 360
8x = 360
x = 360/8
x = 45
Number of boys= 3x = 3 *45 = 135
Number of girls = 5x = 5 * 45 = 225
AOMS school has more boys attending their school.
Ratio of girls attending Aviara Oaks Middle School to girls attending Valley Middle School = 240 : 225
= 48 : 45
Lisa purchased almonds for $3.50 per pound here
de and your estimate
2450 How many pounds of almonds did she
purchase?
On an exam a student earned a grade of 80. On the retake they earned a grade of 100. What is the percent increase in the grade?
Answer:
25%
Step-by-step explanation:
Percentage increase from 80 to 100 making the increase 25%
Answer:
16 percent sorry if im wrong i tried
Step-by-step explanation:
What is the area of the circle that has a diameter of 12
Answer:
113.1 *whatever unit it is in*
Step-by-step explanation:
Answer:
113.10 m squared
$1900 at 9 for 2 years
Answer:
$342
Step-by-step explanation:
Complete question
Find the simple interest on $1900 at 9% for 2 years.
Simple interest PRT/100
Given
Principal P = 1900
Rate R = 9%
Time T = 2years
Substitute
Simple interest = 1900*9*2/100
Simple interest = 19*18
Simple interest = $342
Hence the simple interest on $1900 at 9% for 2 years is $342
What is the volume of
4 m
6 m
10 m
6 m
What is the volume of this composite solid?
Answer:600
Step-by-step explanation:
Santiago’s $2900 monthly budget is represented by the pie chart below. All amounts are in dollars.
What percentage of his monthly budget does Santiago spend on groceries?
A. 16%
B. 11%
C. 6%
D. 13%
Answer
11%
Explanations
Complete question
Doug's monthly budget is represented by the pie chart below. All amounts are
in dollars.
403
Monthly Budget
806
Car Expenses
Housing
Utilities
868
Groceries
496
Savings
Other
341
186
What percentage of his monthly budget does Doug put in savings?
O A. 13%
B. 6%
C. 11%
D. 16%
To get the percentage of his monthly budget does Doug put in savings, first we need to get the total savings
Total savings = 403+806+868+496+341+186
Total money = $3100
Amount spent on savings = $341
Percentage savings = amount spent on savings/Total money × 100%
Percentage savings = 341/3100 × 100
Percentage savings = 341/31
Percentage savings = 11%
Hence the percentage of the total money spent on savings is 11%
Factorise fully the following:
a) x² - 2x
b) 6x2 + 12x
c) 3-9x
d) 4x + 28x
Answer:
Please find pdf attached
Step-by-step explanation:
Sixteen times a number j is no less than -2
How many solutions does this linear system have?
y = 2x-5
-8x - 4y = -20
A one solution: (-2.5, 0)
B one solution: (2.5, 0)
C no solution
D O infinite number of solutions
Answer:
B
Step-by-step explanation:
(2.5,0)
what is the answer to : 1.3(4.9 + 6k)
Answer:
you'd get the expression 6.37+7.8k
select the correct answer
Answer:
I think b is the correct answer
A man goes into a store and says, “If you give me as much money as I have with me now, I will spend $10 in your store.” The store owner agrees, and the man spends the money.
He goes into a second store and again says, “If you give me as much money as I have with me now, I will spend $10 in your store.” Again, the owner agrees, and the man spends the money.
In a third store, he repeats his proposition. The proprietor agrees, and the man spends the money.
At this point, the man has no money left. How much money did he have to begin with?
Answer:
$8.75
Step-by-step explanation:
Let x = the amount the man originally had
The man has $x and says "if you give me $x, I will spend $10."
y = amount he has after 1st proposition = x + x - 10 = 2x - 10
He repeats this procedure, now with $2x-10 in his pocket...
z = amount he has after 2nd proposition = (2x - 10) + (2x - 10) - 10 = 4x - 30
He repeats this procedure, now with $4x-30 in his pocket...but this time he is left with zero dollars...
r = amount he has after 3rd proposition = (4x-30) + (4x-30) - 10 = 8x-70 = 0
8x - 70 = 0,
x = $8.75
Use the slope formula to determine the slope of the line containing the two points.
(-1, -7) and (-6, -3)
A. 10/7
B. -4/5
C. -1/2
D. -5/4
A 21°
B 42°
C 639
D1260
Answer:
D) 126°
Step-by-step explanation:
<G=84
<D=x
<E=180-3x
added all together should equal 180
84+x+180-3x=180
-2x=180-264
-2x=-84
x=42
<FEG=3x=3(42)=126
What is the value of the expression below when n=5
Answer:
-6 (i can explain if its needed)
Step-by-step explanation:
[tex]2 - {n}^{2} + 3 \times 14 - {n}^{2} = \\ 2 - {n}^{2} + 42 - {n}^{2} = \\ 2 - 25 + 42 - 25 = - 6[/tex]
A plane travels 1820 meters at a speed of 260 m/sec. How long did it
take to reach its destination? PLEASE HELP!
Answer:
7 seconds
Step-by-step explanation:
1820/260=7.
Answer:
7m/sec
Step-by-step explanation:
All even numbers
greater than two, can be written
as the sum of two prime numbers
Peter
Give three examples that show that Peter is correct.
Answer:
Step-by-step explanation:
3 + 5 = 8
7 + 11 = 18
11 + 19 = 30
HELP ME PLZ ITS DUE SOON THX
Acetaminophen is a common pain reliever and fever reducer. Here is a graph showing the amount of acetaminophen, in milligrams, in an adult's body at different times after they take a normal dose.
1. What is the vertical intercept? What does it mean in this situation?
2. What fraction of the medicine remained after one hour?
3. Write an equation that represents the amount of medicine, a, after t hours.
Answer:
1.1000
2.3/4
3.f(x)=1000(1/4)^X
Step-by-step explanation:
How do I evaluate this using trigonometric substitution?
∫dx/(81x^2+4)^2
Answer:
[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]
General Formulas and Concepts:
Alg I
Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Pre-Calc
[Right Triangle Only] Pythagorean Theorem: a² + b² = c²
a is a legb is a legc is hypotenuseTrigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]
Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]
TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]
TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]
Calc
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
IP [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
U-Trig Substitution: x² + a² → x = atanθ
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]
Step 2: Identify Sub Variables Pt.1
Rewrite integral [factor expression]:
[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]
Identify u-trig sub:
[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]
Later, back-sub θ (integrate w/ respect to x):
[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]
Step 3: Integrate Pt.1
[Int] Sub u-trig variables: [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]: [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]: [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]: [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]Step 4: Identify Sub Variables Pt.2
Determine u-sub for trig int:
u = 2θ
du = 2dθ
Step 5: Integrate Pt.2
[Ints] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub: [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]Step 6: Triangle
Find trig values:
[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]
[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]
tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
Leg a = 2
Leg b = 9x
Leg c = ?
Sub variables [PT]: [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents: [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite: [tex]c = \sqrt{81x^2 + 4}[/tex]Substitute into trig ratios:
[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]
[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]
Step 7: Integrate Pt.3
[Exp] Sub variables [TR]: [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute: [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]