The correct mixed fraction is 2) 1 [tex]\frac{23}{28}[/tex]
What is mixed fraction and improper function ?
A mixed fraction is one that has both a whole number portion and a proper fraction, and whose value is always larger than 1. A mixed number is, for instance, 3[tex]\frac{2}{5}[/tex]. A fraction is deemed inappropriate if the numerator is consistently greater than or equal to the denominator. 4/3, 7/3, 11/5, etc. are a few instances of incorrect fractions.
Here the given division is,
=> 5 [tex]\frac{2}{3}[/tex] ÷ 3 [tex]\frac{1}{9}[/tex]
=> [tex]\frac{15+2}{3}[/tex] ÷ [tex]\frac{27+1}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] ÷ [tex]\frac{28}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] * [tex]\frac{9}{28}[/tex]
=> [tex]\frac{51}{28}[/tex]
=> 1 [tex]\frac{23}{28}[/tex]
Hence the correct option is 2) 1 [tex]\frac{23}{28}[/tex]
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simplify: 3√45 -4 √225 + √200 - √50
According to the given data we have the following:
3√45 -4 √225 + √200 - √50
Then to simplify we would have to make the following:
[3 × √3 × √3 × √5] - [√5 × √5 × √5] + [√2 × √2 × √2 × √5 × √5] - [√2 × √5 × √5]
=[3 × 3 × √5] - [5 × √5] + [2 × 5 × √2] - [5 × √2]
=3√5 - 5√5 + 10√2 - 5√2
=√5(3 - 5) + √2(10 - 5)
=(-2√5) + 5√2
Therefore, the answer would be 16√5 + 75√2
The product of the ages (in days) of two newborn babies Simran and Jessie in two dayswill be 48 more than the product of their ages today. How old are the babies if Jessie is 2days older than Simran?
Given that:
- The product of the ages (in days) of babies Simran and Jessie in two days
will be 48 more than the product of their ages today.
- Jessie is 2 days older than Simran.
Let be "j" Jessie's age (in days) and "s" Simran's age (in days).
You can set up the following System of Equations using the data given in the exercise:
[tex]\begin{cases}(j+2)(s+2)=js+{48} \\ j={s+2}\end{cases}[/tex]You can use the Substitution Method to solve the system:
1. Substitute the second equation into the first one:
[tex](s+2+2)(s+2)=(s+2)s+48[/tex]2. Solve for "s":
[tex](s+4)(s+2)=s^2+2s+48[/tex][tex](s)(s)+(s)(2)+(4)(s)+(4)(2)=s^2+2s+48[/tex][tex]s^2+2s+4s+8=s^2+2s+48[/tex][tex]\begin{gathered} 4s=48-8 \\ \\ s=\frac{40}{4} \\ \\ s=10 \end{gathered}[/tex]3. Substitute "s" into the second original equation and evaluate:
[tex]\begin{gathered} j=10+2 \\ j=12 \end{gathered}[/tex]Hence, the answer is: Jessie is 12 days old and Simran is 10 days old.
I just need to know the answer for question 12
Given:
The given inequalities are:
[tex]3x+1>7\text{ and 4x}\leq24[/tex]Solving first inequality, we get:
[tex]\begin{gathered} 3x+1>7 \\ 3x>7-1 \\ 3x>6 \\ x>\frac{6}{3} \\ x>2 \end{gathered}[/tex]Solving the second inequality, we get:
[tex]\begin{gathered} 4x\leq24 \\ x\leq\frac{24}{4} \\ x\leq6 \end{gathered}[/tex]Merging the solutions of both inequalities, we get:
[tex]\begin{gathered} x>2\text{ and x}\leq6 \\ \Rightarrow x\epsilon\text{ (2,6\rbrack} \end{gathered}[/tex]So, the graph will be a number line with an open circle at 2 and a closed circle on 6 and shading in between.
Therefore,
Option A is correct.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Write a systems of equations for each problem define variables used. Please show all work.On a table are 20 coin., quarters and dimes. Their value is $3.05 how many of each kind of coin are there?
We have 20 coins in total, lets say that we have X amount od quarters(0.25 dollar) and Y amount of dimes(0.1 dollar), and in total we have $3.05, with this we can write the system:
[tex]X+Y=20[/tex]Wich means that we have 20 coins, and:
[tex]0.25X\text{ + 0.1Y=3.05}[/tex]Thats the amount of money we have.
So, from the first equation, we can isolate X, as follows:
[tex]X=20-Y[/tex]And with that we can substitute X in the second equation, as follows:
[tex]0.25X\text{ + 0.1Y=3.05 }\rightarrow\text{ }0.25(20-Y)\text{ + 0.1Y=3.05 }\rightarrow\text{ }5-0.25Y+0.1Y=3.05[/tex][tex]5-0.25Y+0.1Y=3.05\rightarrow-0.15Y=-1.95\rightarrow Y=13[/tex]So, if Y=13, we have that X=7. So 13 dimes and 7 quarters.
100 POINTS PLE HELP ASAP
A college is currently accepting students that are both in-state and out-of-state. They plan to accept two times as many in-state students as out-of-state, and they only have space to accept 200 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 200 and y > 400
0 < x and y < 200
0 < x ≤ 200 and 0 < y ≤ 400
Answer:
option c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
0 < x and y <200
HELP ME PWEASE (what is A^2 + B^2 =)
YOUR WELCOME FOR THE POINTS
Answer:
i think it is 61
correct me if im wrong
Answer:
a2 + b2 = (a + b)2 -2ab.
Step-by-step explanation:
Your Welcome:)
- 2ab
) In triangle XYZ, angle Y is right angle, and angle X and angle Y are complementary angles.If sin x =3/5 and cos x=4/5 then what is the value of sin y?
A) 3/5
B)4/5
C) 3/4
D)4/3
The value of sin Y is 4/5. The correct option is B) 4/5
Calculating the value of the sine of an angleFrom the question, we are to determine the value of sin Y.
From the given information, we have that
sin X = 3/5
and
cos X = 4/5
Also,
We have that angle X and angle Y are complementary angles.
That is,
X + Y = 90°
From the Trigonometric ratios of complementary angles, we have that
sin Y = cos (90° - Y)
From X + Y = 90°
X = 90° - Y
Therefore,
sin Y = cos X
From the given information,
cos X = 4/5
Hence, sin Y = 4/5
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Persevere with Problems William is 3 feet 1 inch tall and would like to ride a roller coaster. Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller William must be.
Step-by-step explanation:
1 ft = 12 in
he is 3 ft 1 in, that is then 3×12 + 1 = 37 in tall.
so,
37 + x >= 42
and then
x >= 42 - 37
x >= 5 in
Consider the equation 2x+5y=1Identify the slope and y intercept
Solution
Given the equation 2x+5y=1
We are required to Identify the slope and y intercept
The general equation of a straight line is in the form y = mx + c
Where m = slope and c= y-intercept
To solve the problem before us, we need to re-write 2x+5y=1 in the form y = mx + c
[tex]\begin{gathered} 2x+5y=1 \\ 5y=-2x+1 \\ y=-\frac{2}{5}x+\frac{1}{5} \\ \\ Comparing\text{ the resulting equation with y=mx+c} \\ m=-\frac{2}{5},\text{ c=}\frac{1}{5} \end{gathered}[/tex]Thus, the slope = -2/5 while the y-intercept is 1/5
The cross-section of a lean-to shelter is in the shape of a triangle. The base of the triangle is 88 feet more than twice its height. If the area of the triangle is 6060 square feet, determine the length of the base and the height of the triangle in feet.
The length of the base and the height of the triangle are 7.7 feet and 15.7 feet
How to determine the length of the base and the height of the triangleFrom the question, we have the following parameters that can be used in our computation:
Base = 8 feet more than twice the height
Area = 60
This means that
b = 8 + h
A = 60
The area of a triangle is
A = 0.5bh
So, we have
0.5(8 + h)h = 60
This gives
4h + 0.5h² = 60
Rewrite as
0.5h² + 4h - 60 = 0
Using a calculator, we have
h = 7.7
Recall that
b = 8 + h
So, we have
b = 8 + 7.7
Evaluate
b = 15.7
Hence, the base is 15.7 feet
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An arena manager tallies the number of snack items (hot dogs, nachos, and popcorn) sold at each of three concession stands in the arena.
Snack Item
Hot Dogs Nachos Popcorn Total
Concession
Stands Stand A 125 65 40 230
Stand B 218 119 52 389
Stand C 65 52 13 130
Total 408 236 105 749
What is the probability that a customer purchased popcorn, given that they purchased from stand B?
6.9%
13.4%
14.0%
49.5%
The probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.
What is termed as the probability?The term "probability" refers to the likelihood of a specific event (or set of events) occurring, explained on a linear scale from 0 (unlikelihood) to 1 (certainty), as well as as a proportion between 0 and 100%.For the given question;
The data for the selling of the snack items at arena are given;
Snack Item Hot Dogs Nachos Popcorn Total Concession
Stand A 125 65 40 230
Stand B 218 119 52 389
Stand C 65 52 13 130
Total 408 236 105 749
Now the customer purchased the popcorn from stand B.
Thus, total number of snack at stand B = 389
Total number of popcorn at stand B = 52
Thus,
Probability = favourable outcome/total outcome
Probability = 52/386
Probability % = 52/386 × 100
Probability % = 13.4%.
Thus, the probability that a customer purchased popcorn, given that they purchased from stand B is 13.4%.
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17. Testing Lipitor In a clinical trial of the cholesterol drug Lipitor, subjects were partitioned into groups given a placebo or Lipitor doses of 10 mg, 20 mg, 40 mg, or 80 mg. The subjects were randomly assigned to the different treatment groups (based on data from Pfizer, Inc.). would it be a random,systematic, onvience, stratified, or cluster.
Answer:
Stratified
Explanation:
In Stratified Sampling, members of the population are divided into subgroups before a random sample of each group is taken.
Therefore in the case of the clinical trial presented, the sampling method used is stratified.
14 Betsy works as waitress. Today she worked an 8 hour shift, and was paid $ 92.00. Plot
a graph of the amount Betsy earns against the time she works for. Then find how much
Betsy is paid per hour. Write an equation using Y = MX + B Form.
Answer:
11.50 per hour
Step-by-step explanation:
Y = 92
8 = Mx
Y = mx
92 = m(8)
m = 11.50 per hour
Gary makes $7.48 an hour. He grossed $310.42 last week. How many hours did he work?
Answer:
Gary worked 41 and a half hours
Step-by-step explanation:
$310.42 divided by $7.48 per hour = 41.5 hours
Question 12(Multiple Choice Worth 1 points)(07.04 LC)Factor completely 36x² - 49.(3x + 7)(12x-7)(3x-7)(12x+7)(6x-7)(6x-7)(6x + 7)(6x-7)
The factor the binomial
[tex]a^2-b^2[/tex]Find the square root of a and the square root of b, then put them as the product of the sum and difference of these square roots
[tex]\begin{gathered} \sqrt{a^2}=a \\ \sqrt{b^2}=b \\ a^2-b^2=(a+b)(a-b) \end{gathered}[/tex]We will use this rule to factor in the given expression
[tex]36x^2-49[/tex]Find the square root for each term
[tex]\begin{gathered} \sqrt{36x^2}=6x \\ \sqrt{49}=7 \end{gathered}[/tex]Write the two factors
[tex]36x^2-49=(6x+7)(6x-7)[/tex]The answer is the last choice (6x + 7)(6x - 7)
Make a table of values for the function Y=-4x
The table of values for the function y = -4x.
The table is attached below-
Hence, the values for the function is giiven below
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Solve for n: 2n = n + 3 O A. 1 O O c. 3 3 OD. 5 E 6
Step 1: Problem
2n = n + 3
Step 2: Concept
Collect like terms and find the value of x.
2n = n + 3
2n - n = 3
n = 3
Step 3: Final answer
n = 3
Solve the system of equations :-6x - y = -16-6x -5y = -8
The given system of equation are :
-6x - y = -16
-6x -5y = -8
On subtracting both the equation we get :
-6x -y -(-6x -5y) = -16 -(-8)
-6x -y +6x +5y = -16 +8
-6x + 6x +5y -y = -8
4y = -8
4y = -8
Divide both side by 4:
4y/4 = -8/4
y = -2
Substitute the value of y =- 2 in the any one equation:
-6x - y = -16
-6x - (-2)= -16
-6x + 2 = -16
-6x = -16 -2
-6x = -18
x = 3
Answer : x = 3, y = -2
simplify and solve the following linear equations.15 (Y - 4 - 2) Y - 9 + 5 (Y + 6)=0
Solution
We want to solve
[tex]\begin{gathered} 15(y-4)-2(y-9)+5(y+6)=0 \\ Exapnd\text{ the brackets } \\ 15y-60-2y+18+5y+30=0 \\ 15y-2y+5y-60+18+30=0 \\ 18y-12=0 \\ 18y=12 \\ \text{Divide both sides by 18} \\ \frac{18y}{18}=\frac{12}{18} \\ y=\frac{12}{18} \\ y=\frac{2}{3} \\ \\ \text{The answer is y = }\frac{2}{3} \end{gathered}[/tex]Find the decay factor from the function y = 500(0.75)3.
The given function is:
[tex]y=500(0.75)^3[/tex]It is required to find the decay factor.
Recall that the standard form of an exponential decay function is given as:
[tex]y=a(b)^x[/tex]Where a>0, 0and b is the decay factor.
Compare the given equation to the standard form.
It can be observed that b=0.75. Hence, the decay factor is 0.75.
The answer is 0.75.help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
pls helpp
I dont understand this
Answer:
third expression
Step-by-step explanation:
the surface area (SA) is the area of the 6 faces.
Note that opposite faces are congruent.
the surface area is the the area of each face multiplied by 2 , since they are congruent.
SA = 2(front area ) + 2(side area ) + 2(area of base)
= 2(5 × 7 ) + 2(4 × 7 ) + 2(4 × 5 ) ← third option
= 2(35) + 2(28) + 2(20)
= 70 + 56 + 40
= 166 cm²
What is the equation of the line that passes through the points (4, -3) and (5, 0) in point-slope form? y - 5 = -1/3(x - 0) y - 4 = -3(x + 3) y - 0 = 1/3(x - 5) y + 3 = 3(x - 4)
Answer:
d. y+3=3(x-4)
Step-by-step explanation:
graphing both points you see a slope of 3. If you continue to follow the slope of 3, you will find the y-intercept is -15.
y+3=3(x-4)
y+3=3x-12
y+3(-3)=3x-12(-3)
y=3x-15 (slope intercept form)
Miranda has $50 to buy 6 swim caps for the members of a swim team.
Which expression shows the amount of money she will have left if each swim cap costs c dollars?
Answer:
50÷6=8 R2
Step-by-step explanation:
8
6 ⟌50 R2
- 0
-------------
50
-48
--------------
2
So, Miranda will have $8 left to buy.
5. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture?
The picture represents isosceles triangle theorem.
From the figure :
It is represented that two sides are equal.
And the angles opposite to this two equal sides are equal.
So it is a isosceles triangle.
Isosceles triangle:
If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.
Therefore the picture represents isosceles triangle theorem.
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Absolute value can never be negative,
true or false?
Answer:
Yes, an absolute value can never be false. So, the answer is true.
Which equation represents the line that is parallel to y=3/4x + 7 and passes through (-12,36)?
Answer:
If it is parallel:m parallel line=m line given, so:
mparallel=3/4
And it passes through one point given, so we use the formula: y-y0=m(x-x0)
so: y-36=3/4(x+12)
y=3/4x+9+36
y=3/4x+45 is the correct answer.
9- (4x + 4) = 3x - 10 + 8x
Answer: 1=x
Step-by-step explanation:
9-4x-4=3x-10+8x
9-4+10=3x+8x+4x
15=15x
1=x
Expand the brackets :
9 - 4x - 4 = 3x - 10 + 8x
-> 9 - 4x - 4 - (3x - 10 + 8x) = 0
-> 9 - 4x - 4 - 3x + 10 - 8x = 0
-> (9 - 4 + 10) - (4x + 3x + 8x) = 0
-> 15 - 15x = 0
15x = 15
x = 1
Might be confusing so just leave a comment if you don't understand (because I do the more detailed way really ;-;)
You used `14` ounces of cheese to make `2` pizzas.
How much cheese do you need for `3` pizzas?
Answer:
You need 21 ounces of cheese for 3 pizzas.
Step-by-step explanation:
If you use 14oz for 2 pizzas, then if you divide it by 2, you have 7oz for 1 pizza.
Now multiply by 3 to get 21oz for 3 pizzas.