Answer:
-5x + 3(10x - 8)= 51
-5x + 30x - 24 = 51
25x - 24 = 51
25x = 75
x = 3
y = 10(3) - 8
y = 30 - 8
y = 22
(3, 22)
The area of the net the team uses is no more than 107.25 ft2. The width of the net is 3.25 feet.
Which inequality can be used to find the possible lengths of the volleyball net?
Answer:
The inequality is [tex]l\times (3.25)\leq 107.25[/tex]
Step-by-step explanation:
Given: Area of volleyball net= [tex]107.25 ft^{2}[/tex]
Width of Volleyball net= [tex]3.25 \ ft[/tex]
Considering the volleyball net is in rectangular shape and l and w is length and width respectively.
Area of rectangle= [tex]l\times w[/tex]
Now, using formula to form inequality
⇒ [tex]l\times (3.25)\leq 107.25[/tex]
Next, using the inequality to find length of Volleyball net.
∴ [tex]l\times (3.25)\leq 107.25[/tex]
Dividing both side by 3.25
⇒ [tex]l= \frac{107.25}{3.25} = 33\ ft[/tex]
∴ l= 33 ft
The possible length of Volleyball net is 33 ft.
Answer:
b
Step-by-step explanation:
In the half-life function Q(t)=28550⋅((34)h)(th) Q ( t ) = 28550 ⋅ ( ( 3 4 ) h ) ( t h ) , what is the half-life, h h , if (34)h=12 ( 3 4 ) h = 1 2 ?
The half-life h is calculated to be approximately 2.41.
To determine the half-life h from the given half-life function:
[tex]\[ Q(t) = 28550 \cdot \left( \frac{3}{4} \right)^{\frac{t}{h}} \][/tex]
we need to solve for h in the equation:
[tex]\[ \left( \frac{3}{4} \right)^h = \frac{1}{2} \][/tex]
To solve for h , we take the natural logarithm (ln) of both sides of the equation:
[tex]\[ \ln \left( \left( \frac{3}{4} \right)^h \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Using the logarithmic property [tex]\(\ln(a^b) = b \ln(a)\)[/tex], we get:
[tex]\[ h \ln \left( \frac{3}{4} \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Now, solve for h :
[tex]\[ h = \frac{\ln \left( \frac{1}{2} \right)}{\ln \left( \frac{3}{4} \right)} \][/tex]
Calculate the natural logarithms:
[tex]\[ \ln \left( \frac{1}{2} \right) = \ln(0.5) \approx -0.6931 \\\[ \ln \left( \frac{3}{4} \right) = \ln(0.75) \approx -0.2877 \][/tex]
Now, divide these values to find h :
[tex]\[ h = \frac{-0.6931}{-0.2877} \approx 2.41 \][/tex]
So, the half-life h is approximately:
[tex]\[ h \approx 2.41 \][/tex]
Therefore, the half-life h rounded to the nearest hundredth is:
h = 2.41
PLEASE SOMEONE HELP ME ON THIS QUESTION!!!
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
Im going to assume a faction greater than one means an improper fraction.
Converting [tex]2 \frac{2}{6}[/tex] gets [tex]\frac{14}{6}[/tex] which simplified is [tex]\frac{7}{3}[/tex]
plz help super fast 4 mins
Answer:
A. 10%
Step-by-step explanation:
Let events A nad B be:
A = an employee is a female
B = an employee is under the age of 30.
Use formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
There are 200 employees, 150 of them are female, then
[tex]P(A)=\dfrac{150}{200}=\dfrac{3}{4}=0.75[/tex]
There are 200 employees, 40 of them are under the age of 30, then
[tex]P(B)=\dfrac{40}{200}=\dfrac{1}{5}=0.2[/tex]
The probability of randomly selecting an employee who is a female or under the age of 30 is 85%, then
[tex]P(A\cup B)=0.85[/tex]
Thus,
[tex]0.85=0.75+0.2-P(A\cap B)\\ \\0.85=0.95-P(A\cap B)\\ \\P(A\cap B)=0.95-0.85=0.1[/tex]
Therefore, the probability of randomly selecting an employee who is a female and under the age of 30 is 0.1 or 10%.
During a basketball practice, Mai attempted 49 free throws and was on 25% of them. How many successful free throws did she make?
Mai made 12 successful free throws.
Step-by-step explanation:
Given,
Free throws made by Mai = 49 free throw
Successful throws = 25%
Number of successful throws = 25% of free throws
Number of successful throws = [tex]\frac{25}{100}*49[/tex]
Number of successful throws = [tex]\frac{1225}{100} = 12.25[/tex]
Rounding off to nearest whole number;
Number of successful throws = 12
Mai made 12 successful free throws.
Keywords: percentage, division
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What is the equation of a line that is parallel to y=5/6x-10 and passes through (12,8)?
Answer:
y-8=5/6(x-12)
Step-by-step explanation:
y-y1=m(x-x1)
y-8=5/6(x-12)
The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].
Given that,
The equation of the line is,
[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]
It passes through the point (12, 8).
We have to determine
The equation of the line is parallel to the given line.
According to the question,
The equation of the line is,
[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]
The slope of the line [tex]\rm m_1[/tex] is 5/6.
If the two lines are parallel to each other then the slope of these lines is the same.
[tex]\rm m_1 = m_2\\\\\dfrac{5}{6} = \dfrac{5}{6}[/tex]
Therefore,
The equation of line passes through the point (12, 8) is,
[tex]\rm( y -y_1) = m (x-x_1)\\\\(y-8) = \dfrac{5}{6} (x-12)\\\\6 (y-8) = 5(x-12)\\\\6y-48=5x-60\\\\6y = 5x-60+48\\\\6y = 5x-12\\\\y = \dfrac{5}{6}x- \dfrac{12}{6}\\\\y = \dfrac{5}{6}x-2[/tex]
Hence, The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].
For more details refer to the link given below.
https://brainly.com/question/9351049?
What is the value of x in the equation 5x 3-4x2
Answer:
x^2(5x-4)
Step-by-step explanation:
5x^3-4x^2=x^2(5x-4)
Select all the expressions with a product less than 2/3.
4 and 1/8 x 2/3
2/3 x 2/3
2/3 x 2
5/6 x 2/3
The expressions with a product less than 2/3 are:
2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th
Step-by-step explanation:
Let us revise some fact about the product of two numbers
If x is multiplied by y where y > 1, then the product is greater than x (Ex: if x is 3/4 and y is 2, then xy = (3/4)(2) = 3/2 which is greater than 3/4)If x is multiplied by y where 0 < y < 1, then the product is less than x (Ex: if x = 2/5 and y = 1/3, then xy = (2/5)(1/3) = 2/15 which is less than 2/5)We need to select all the expressions with a product less than 2/3
∵ 4 and 1/8 × 2/3
- 4 and 1/8 means mixed number [tex]4\frac{1}{8}[/tex]
∵ [tex]4\frac{1}{8}[/tex] > 1
- That means the product of it and 2/3 will be greater than 2/3
as the first fact above
∴ [tex]4\frac{1}{8}[/tex] × [tex]\frac{2}{3}[/tex] > [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] is between 0 and 1
- That means the product of it and 2/3 will be less than 2/3
as the second fact above
∴ [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{2}{3}[/tex] × 2
∵ 2 > 1
- That means the product of it and 2/3 will be greater than 2/3
as the first fact above
∴ [tex]\frac{2}{3}[/tex] × 2 > [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex]
∵ [tex]\frac{5}{6}[/tex] is between 0 and 1
- That means the product of it and 2/3 will be less than 2/3
as the second fact above
∴ [tex]\frac{5}{6}[/tex] × [tex]\frac{2}{3}[/tex] < [tex]\frac{2}{3}[/tex]
The expressions with a product less than 2/3 are:
2/3 × 2/3 and 5/6 × 2/3
Learn more:
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Only the expressions 2/3 x 2/3 and 5/6 x 2/3 have products less than 2/3, with products of 4/9 and 5/9 respectively.
To determine which expressions have a product less than 2/3, each expression must be evaluated separately:
4 and 1/8 x 2/3 = 33/8 x 2/3
2/3 x 2/3 = 4/9
2/3 x 2 = 4/3
5/6 x 2/3 = 10/18 or 5/9
After simplifying, the expressions that yield a product less than 2/3 are:
2/3 x 2/3 = 4/9, as 4/9 is less than 6/9 (2/3)
5/6 x 2/3 = 5/9, which is also less than 6/9 (2/3)
The expressions 4 and 1/8 x 2/3 and 2/3 x 2 are both greater than 2/3.
5x+3+2y+x in expression
Answer:
6x+2y+3
Step-by-step explanation:
5x+3+2y+x
6x+2y+3
If (10,3) and (6,31) are two
anchor points on a trend line,
then find the equation of the
line.
Answer:
y = - 7x + 73
Step-by-step explanation:
y = mx + b m: slope b: y intercept
m = (y-y') / (x-x') = (31-3) / (6-10) = 28 / - 4 = -7
b = y - mx = 3 - (-7) x 10 = 73
equation: y = -7x + 73
check: 31 = -7 x 6 +73 = -42 + 73 = 31 (6,31)
Four less than the product of two and a number
Answer:
2x - 4
Step-by-step explanation:
Write out the equation:
(2 * x) - 4
Simplify
2x - 4
:)
Fifty students in the seventh grade are trying to raise at least $2000 for sports supplies. They already raised $750. How much should each student raise in order to meet the goal? Write your answer as an inequality.
Answer:
x ≥ 25
Step-by-step explanation:
In the seventh grade, fifty students are trying for sports supplies to raise at least $2000. They already have $750.
Let us assume that each student has to raise $x more to meet the goal.
Then, a total of 50 students will raise $50x more.
Therefore, the inequality to solve for x will be
750 + 50x ≥ 2000
⇒ 50x ≥ 1250
⇒ x ≥ 25 (Answer)
Final answer:
Each seventh grade student should raise at least $25 in order to collectively meet the goal of raising $2000 for their sports supplies after having already raised $750.
Explanation:
The goal amount for the seventh grade sports supplies fundraiser is $2000. They have already raised $750, leaving them with $1250 still needed to reach their goal. If there are 50 students working on the fundraiser, we can set up an inequality to determine how much money each student should raise minimally to meet the goal of $2000. Here's the inequality:
Let x be the amount each student needs to raise.
50x + $750 ≥ $2000
To solve for x, we subtract $750 from both sides of the inequality:
50x ≥ $2000 - $750
50x ≥ $1250
Now divide both sides by 50 to find the amount each student should raise:
x ≥ $1250 / 50
x ≥ $25
Therefore, each seventh grade student should raise at least $25 to meet the $2000 goal.
I need help please and thanks
Answer:
10
Step-by-step explanation:
n is the number of selections and k the number selected, that is
n = 5 and k = 2
note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1, thus
[tex]\frac{5(4)(3)(2)(1)}{2!(5-2)!}[/tex]
= [tex]\frac{120}{2(1)3(2)(1)}[/tex]
= [tex]\frac{120}{2(6)}[/tex]
= [tex]\frac{120}{12}[/tex]
= 10
On a number line, what number is 2/3 of the way from 7 to 13?
Answer:
That would be about 11.667
The number that is 2/3 of the way from 7 to 13 on a number line is 11. This is found by calculating 2/3 of the distance between the two numbers and adding it to the starting number.
To find the number that is 2/3 of the way from 7 to 13 on a number line, you first calculate the distance between the two numbers, which is 13 - 7 = 6. Then you take 2/3 of that distance, which is 2/3 * 6 = 4. Lastly, you add this result to the starting number, in this case, 7, giving you 7 + 4 = 11. Therefore, the number that is 2/3 of the way from 7 to 13 is 11.
Jade uses 8 cups of flour to make 24 muffins at that rate how much flour will it take to make 30 muffins
Answer:
10 cups
Step-by-step explanation:
First, we need to find the unit rate. 24/8 equals to 3. 3 is the amount of flour per cupcake. 24 + 3= 27 + 3= 30. You added twice to get to 30. 8+2=10
Which television would cost you less money? A $429 television set with a 20% discount or a television set with no discount for $359?
Answer:
get the $429 with 20% off cuz its really only $343.2
Step-by-step explanation:
100%-20%=80%
80%=0.8
429x0.8=343.2
Find the measure of each numbered angle.
Answer:
m∠1 = 50°
m∠2 = 88°
Step-by-step explanation:
Each triangle's angles have to add up to 180°. Use supplementary angles theorem to help solve.
Answer:
2.) m/_1 = 50
3. )m/_2=88
Step-by-step explanation:
2.) the line that the exterior angle 140 is on is a straight line. this means it is 180 degrees. 180 - 140 = 40. the box in the left corner means it is a right angle or 90 degrees. evey triangle is 180 degrees so add 40 and 90 to get 130 and then subtract 130 from 180 to get 50 which is the angle number 1.
3.)the line 120 is on is a straight line so we do 180 minus 120 to get the angle inside. it is 60. 60 +32 = 92. 180 - 92 is 88 degrees.
Simply the expression 5a + 7 +3a -2
Answer:
8a+5
Step-by-step explanation:
Like terms and yea
Answer: 8a + 5
Step-by-step explanation:
Combining like terms makes you add 5a + 3a and +7 - 2
The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which of the following describes the domain of (g o f) (x)?
all real values except x not-equals negative 3 and the x for which f (x) not-equals 7
all real values except x not-equals negative 3 and the x for which f (x) not-equals negative 3
all real values except x not-equals 7 and the x for which f (x) not-equals 7
all real values except x not-equals 7 and the x for which f (x) not-equals negative 3
Answer:
The last is the correct option
"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"
Step-by-step explanation:
Domain and Range of Functions
Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.
We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then
[tex]g\circ f=g(f(x))[/tex]
is the composite function of f and g.
We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.
Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.
Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.
Thus, the domain of [tex]g\circ f[/tex] is
All real numbers except x=7 and those where f(x)=-3
The last is the correct option
In a school election, Juan received 4 times as many votes as Wayne, Neal recurved twenty less votes than Juan, and Kerry got half as many votes as Neal. The total votes cast in the election was 1,202. How many votes did Wayne receive?
Votes received by Wayne is 112
Solution:
To find: votes received by Wayne
Let the vote received by Wayne be "x"
Juan received 4 times as many votes as Wayne
Therefore,
Juan votes = 4 times as many votes as Wayne
Juan votes = 4x ---- eqn 1
Neal received twenty less votes than Juan
Neal votes = twenty less votes than Juan
Neal votes = Juan votes - 20
Neal votes = 4x - 20 ---- eqn 2
Kerry got half as many votes as Neal
Kerry votes = half of neal votes
Kerry votes = [tex]\frac{4x - 20}{2}[/tex] ---- eqn 3
The total votes cast in the election was 1,202
Wayne votes + Juan votes + Neal votes + Kerry votes = 1202
Plug in eqn 1 , eqn 2, eqn 3
[tex]x + 4x + 4x - 20 + \frac{(4x - 20)}{2} = 1202\\\\2x + 8x + 8x - 40 + 4x - 20 = 1202 \times 2\\\\22x - 60 = 2404\\\\22x = 2404 + 60\\\\22x = 2464\\\\x = 112[/tex]
Therefore votes received by Wayne is 112
A square has a perimeter of 148 inches. How do you find the length of the diagonal of the square?
Answer:
52.33 inches
Step-by-step explanation:
Multiply the length of one side by the square root of 2.
In this case: 37, you would divide that by the square root of 2.
Hope this helps!
What Is the slope of y=3/4x-7
Answer:
[tex]m=\frac{3}{4}[/tex]
Step-by-step explanation:
This equation is in the form of y=mx+b
In this equation, m is the slope. m is the coefficient of x.
In the equation, [tex]y=\frac{3}{4} x-7[/tex]
[tex]m=\frac{3}{4}[/tex], which is the slope.
Answer:
m = 3/4
Step-by-step explanation:
This equation is in the form of y=mx+b
In this equation, m is the slope. m is the coefficient of x.
In the equation, y=\frac{3}{4} x-7
m=\frac{3}{4}, which is the slope.
A sequence is defined by the recursive formula f(n+1)=f(n)-2. If f(1)=18, what is f(5)?
Answer:
[tex]f(5)=10[/tex]
Step-by-step explanation:
A sequence is defined by the recursive formula [tex]f(n+1)=f(n)-2[/tex]
If [tex]f(1)=18,[/tex] then
for [tex]n=1: f(2)=f(1+1)=f(1)-2=18-2=16[/tex]
for [tex]n=2: f(3)=f(2+1)=f(2)-2=16-2=14[/tex]
for [tex]n=3: f(4)=f(3+1)=f(3)-2=14-2=12[/tex]
for [tex]n=4: f(5)=f(4+1)=f(4)-2=12-2=10[/tex]
Answer:
10!
Step-by-step explanation:
During ski season,the owner of ski shop has determined that the number of customers in a day is greater then or equal to 50 more then the temperature(Fahrenheit)
The question is incomplete. Here is the complete question:
During ski season,the owner of ski shop has determined that the number of customers in a day is greater than or equal to 50 more then the temperature(Fahrenheit) . Write an inequality for the problem and determine the constraints on the variables.
Answer:
[tex]N\geq T+50[/tex]
Step-by-step explanation:
Let the number of customers be 'N' and the temperature in Fahrenheit be 'T'.
Given:
Number of customers is related to temperature in Fahrenheit as:
Number of customers is greater than or equal to 50 more than the temperature in Fahrenheit. This means,
[tex]N\geq T+50[/tex]
Now, since 'N' represents number of customers and number can never be a negative quantity. So, the only constraint for this inequality is that the number of customers must be greater than or equal to 0.
So, [tex]N\geq 0[/tex]
This table shows equivalent ratios which ratios are equivalent to the ratios in the table check all that apply ?
Answer: 40:8 and 20:4
Step-by-step explanation :It matches up if you multiply both top and bottom with 8 to get 40:8 and multiply with 4 to get 20:4 .
Answer:
A and E
Step-by-step explanation:
Please can any one please help me with both of these
Answer:
Question 3: [tex]4x^3+x^2-12x-3[/tex]
Question 4: [tex]\frac{1}{2x}, x\neq 0[/tex]
Step-by-step explanation:
Question 3
g(x) * h(x) means to multiply both the functions given.
Also note the distributive property:
[tex](a+b)(n+p)=an+ap+bn+bp[/tex]
Now, lets multiply:
[tex]g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3[/tex]
The 2nd answer choice is right
Question 4
[tex](\frac{f}{g})(x)[/tex] means to divide both the functions and simplify, if possible. Lets do this:
[tex](\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}[/tex]
This is the correct answer.
The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.
We know we cannot divide by 0, so what makes this fraction division by 0??
If we put x = 0, the function is undefined. So x CANNOT be 0.
Third answer choice is right.
A rectangular swimming pool had a length twice as long as it’s width. The pool has a sidewalk around it that is 2 feet wide. Write an expression that would help you find the area of the pool and it’s sidewalk.
Answer:
Area = [tex]2w^2+12w+16[/tex]
Step-by-step explanation:
We let the width of the pool be "w"
We know the length is twice as long as width, so the length is:
2w
So,
Width = w
Length = 2w
Since a sidewalk with 2 feet width goes around the pool completely, the area enclosed by pool + sidewalk would have 2 feet around it, so its length and width would be:
Width = w + 2 + 2 = w + 4
Length = 2w + 2 + 2 = 2w + 4
The area of a rectangular region is always length * width, so the expression for area of pool and sidewalk would be:
[tex](w+4)(2w+4)\\=2w^2+4w+8w+16\\=2w^2+12w+16[/tex]
If we let the width of the swimming pool be "w", the expression for the area of pool and sidewalk is:
Area = [tex]2w^2+12w+16[/tex]
what is the working out for 5x+3=2x+15
The solution is x = 4
Step-by-step explanation:
The given equation is a linear equation so it will have only one equation
Given equation is:
[tex]5x+3=2x+15[/tex]
Subtraction property of equality:
[tex]5x+3-3 = 2x+15-3\\5x = 2x+12[/tex]
Subtraction property of equality:
[tex]5x-2x = 2x-2x+12\\3x = 12[/tex]
Division Property of Equality:
[tex]\frac{3x}{3} = \frac{12}{3}\\x = 4[/tex]
Hence,
The solution is x = 4
Keywords: Linear equation, variables
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See if you're a genius by answering this question!
A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce
cans of the same soda costs $2.99. Calculate the unit price (price/ounce) of each
item and determine which is the better bargain. Explain your answer.
Answer:
Do you know the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
67.6 oz cost $ 1.89
unit rate is : 1.89 / 67.6 = 0.027....rounds to 3 cents per oz
12 twelve oz cans.....thats (12 * 12) = 144 oz....for 2.99
2.99 / 144 = 0.0207....rounds to 2 cents per oz
the better bargain would be the 12 twelve oz cans because u save one penny more per oz then when ur buying the 2 liter bottle
What is a positive coterminal angle to -32° that is between 500° and 1000° and a negative
coterminal angle to -32° that is between – 500° and -50°?
Positive coterminal angle = 688 degrees
Negative coterminal angle = -392 degrees
Solution:
Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Positive coterminal angle:
The positive coterminal angle of [tex]-32^{\circ}[/tex] is given as:
We have to find positive coterminal angle between 500° and 1000°
Between 500° and 1000° there is an angle which is coterminal to 0°:
2 x 360° = 720°
positive coterminal angle = [tex]-32^{\circ} + 720^{\circ} = 688^{\circ}[/tex]
Negative coterminal angle:
We have to find negative coterminal angle between – 500° and -50°
Negative coterminal angle = [tex]-32^{\circ} - 360^{\circ} = -392^{\circ}[/tex]