The unit rate for $210 of 17 ft² rounded to the nearest hundredth is equal to 12.
What is a conversion factor?A conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal numerical value must be used when it is necessary to perform any mathematical conversion.
Conversion:
210 dollars = 17 square feet.
x dollar = 1 square feet.
Cross-multiplying, we have:
17x = 210
x = 210/17
x = 12.35 ≈ 12
Therefore, the unit rate is equal to 12.
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If Tristan borrows $4000 at an interest rate of 7.4% with a loan term of 3 years, how much does Tristan pay interest
The amount of Interest Tristan pays is $955.2
Given:
Tristan borrows $4000 at an interest rate of 7.4% with a loan term of 3 years.
we are asked to determine the interest Tristan pays for it:
we know:
P = $4000
r = 7.4%
t = 3 years.
Evaluate :
I = 4000(1+7.4%)³ - 4000
I = 4000(1+0.074)³ - 4000
I = 4000(1.074)³ - 4000
I = 4000(1.2388) - 4000
I = 4955.2 - 4000
I = 955.2
Hence we get the required interest as $955.2
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The average mass of a man is 84 kg and of a woman is 70 kg
a lift can safely carry 620 kg
work out the maximum number of people the lift can safely carry
The maximum number of people the lift can safely carry is 8 people.
Given that, the average mass of a man is 84 kg and of a woman is 70 kg.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Now, average = (84+72)/2
= 156/2
= 78
Let the number of people in the left be n.
So, 78n≤620
Divide 78 to both the sides of the inequality
78n/78≤620/78
⇒ n≤7.9
⇒ n≤8
Therefore, the maximum number of people the lift can safely carry is 8 people.
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I need help to solve this please!!
Answer:
Adult is 10$ and Child is 7$.
Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.
Hope this helps!
Step-by-step explanation:
2x + 4y = 48
5x + 2y = 64
2x + 4y = 48
10x + 4y = 128
( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )
8x = 80
x = 10
2 ( 10 ) + 4y = 48
20 + 4y = 48
4y = 48 - 20
4y = 28
y = 7
By the triangle sum theorem, the sum of the angles in a triangle is equal to Response area. Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=64°.
The required measure of the angle is m∠A=64°.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
,
Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°
Thus, the required measure of the angle is m∠A=64°.
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Scott will purchase a new computer on an installment plan. The computer costs $2,300 and requires a 15% down payment.
a.) How much is the down payment?
The value of the down payment for the car is $345.
How to calculate the.dow payment?From the information, Scott will purchase a new computer on an installment plan and the computer costs $2,300 and requires a 15% down payment.
The value of the down payment will be:
= Down payment percentage × Total cost
= 15% × $2300
= 0.15 × $2300
= $345
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Use the diagram and the given angle measure to find the other three angle measures
By using the diagram and the given angle measure we get that:
if, m∠1 = 143°
then, m∠2 = 37°
m∠3 = 143°
m∠4 = 37°
What is angles?
An angle is formed when two straight lines or rays meet at a common endpoint.
What is Properties of Congruence?
Reflexive Property:For all angles A ,
∠A≅∠A .
An angle is congruent to itself.
Symmetric Property:For any angles A and B ,
if ∠A≅∠B , then ∠B≅∠A .
Order of congruence does not matter.
Transitive Property:For any angles A,B, and C ,
if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .
If two angles are both congruent to a third angle, then the first two angles are also congruent.
I assume that, this refers to two intersecting lines which form four angles.
∠1 and ∠2 are supplementary angles whose sum is 180°.∠1 + ∠2 = 180°
143° + ∠2 = 180°
∠2 = 180° - 143°
∠2 = 37°.
∠1 and ∠3 are vertical angles so do with ∠2 and ∠4.Therefore, it is easy to find their measures because vertical angles are congruent in measure.It means that, ∠1 = ∠3 =143° (properties of congruency)
and ∠2 = ∠4 =37° (properties of congruency).
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3x - 2 when x=4
please be quickkkkkkkk
Answer:
10
Step-by-step explanation:
substitute x = 4 into the expression
3x - 2 = 3(4) - 2 = 12 - 2 = 10
Answer: 10
Step-by-step explanation:
4 × 3 = 12
12 - 2= 19
Hope it helps
4) Simplify the expression and identify any restrictions on x.
Answer:
6X/X^2-2X+1
Step-by-step explanation:
x
2
−3x+2
9x
2
+18x
÷
2x−4
3x
2
+3x−6
Divide
x
2
−3x+2
9x
2
+18x
by
2x−4
3x
2
+3x−6
by multiplying
x
2
−3x+2
9x
2
+18x
by the reciprocal of
2x−4
3x
2
+3x−6
.
(x
2
−3x+2)(3x
2
+3x−6)
(9x
2
+18x)(2x−4)
Factor the expressions that are not already factored.
3(x−2)(x+2)(x−1)
2
2×9x(x−2)(x+2)
Cancel out 3(x−2)(x+2) in both numerator and denominator.
(x−1)
2
2×3x
Expand the expression.
x
2
−2x+1
6x
An ocicat eats $\frac 35$ of a pound of food daily. How many whole ocicats can a $19\frac 12$-pound bag of food feed for one week?
Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .
In the question ,
it is given that
the amount of food that the ocicat eats in 1 day = 3/5 pound
So , the amount of food that the ocicat eats in 1 week = (3/5) × 7 = 21/5
we have to find the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed .
So ,
the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed = [tex]19\frac{1}{2}[/tex] ÷ 21/5
= (19*2+1)/2 ÷ 21/5
= 39/2 × 5/21
= (39 × 5)/(2 × 21)
= 195/42
= 65/14
= [tex]4\frac{9}{14}[/tex] ocicats
since the number of ocicats cannot be in fraction ,
so number of ocicats = 4
Therefore , Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .
The given question is incomplete , the complete question is
An ocicat eats 3/5 of a pound of food daily. How many whole ocicats can a [tex]19\frac{1}{2}[/tex] -pound bag of food feed for one week?
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Can someone help Solve for x.
Find x if AC= 17, BD = 2x - 6, AD= x + 16, and BC = 6
Answer:
Hey, hope it helps my friend
Step-by-step explanation:
In the image
which are the solutions of x2= -5x +8
1. Which is an example of an experiment? (1 point)
OA company asks its website users to rate its new features to navigate the site.
O Researchers working for a company test their new sneaker design to see if it helps athletes run faster.
OA scientist watches a group of local birds to see what type of tree they prefer to make their nests in.
An ice cream company asks people to identify their top three ice cream flavors.
An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.
What is an experiment?An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated
Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.
In this case, testing the new sneakers is an experiment.
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List the independent and dependent variables
H(x)=3+0.5x
x is the independent variable and H(x) is the dependent variable
How to determine independent and dependent variables?
A dependent variable is a variable whose value depends upon independent variables.
An independent variable is a variable that does not depend on any other variable for its value.
For example, in an expression, y = 3x + 2, x is an independent and y is a dependent variable because y depends on x for its value
Given: H(x) = 3+0.5x
Therefore, x is the independent variable and H(x) is the dependent variable because it is a function of x
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1. If f(2)= -5, what does 2 represent?
2. If f(2)=-5, what does -5 represent?
3. What does f(2)= -5 mean?
In the function f(2)= -5, 2 is the preimage of the function and 5 is an image of the function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Suppose that f(a) = b
In that case, element "b" is the image of element "under the function," while element "a" is the preimage of element "under the function."
In the given function f(2)= -5
2 is the preimage of the function and 5 is an image of the function.
Hence, the 2 is the preimage of the function and 5 is an image of the function.
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(jk−1)÷j when j=−4 and k=−0.9
The numerical value of the expression ( jk−1 )÷j when j=−4 and k=−0.9 is -0.65.
What is the numerical value of the given expression?Given the expression in the question;
( jk − 1 ) ÷ jj = -4k = -0.9To determine the numerical value of the expression, plug in the values of j and k and then simplify.
( jk − 1 ) ÷ j
Plug in j = -4 and k = -0.9
( jk − 1 ) ÷ j
( (-4 × -0.9) − 1 ) ÷ (-4)
Simplify
( 3.6 − 1 ) ÷ (-4)
( 2.6 ) ÷ (-4)
-0.65
Therefore, the value of the expression is -0.65.
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Find the Length of X , please show how you found your answer
The length of the x is 4.8 units
In the given figure
There is one circle and 2 chords
The chord of the circle is defined as the line segment joining any two points one the circumference of the circle
There are two chords in the figure, those are BD and AC
We know that
DE × EB = AE × EC
This is the rule of chords in the circle
The length of DE = 10 units
The length of EB = x units
The length of AE = 6 units
The length of EC = 8 units
Substitute the values in the equation
10 × x = 6 × 8
10x = 48
x = 48/10
x = 4.8 units
Hence, the length of the x is 4.8 units
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Help Please!
Solve the inequality and graph it’s solution.
The solution of given inequality is x≤-2.
What is inequality?
Inequality (mathematics), a relation between two numbers or quantities indicating which of them is greater or smaller. An inequality is denoted by the symbol <, which is drawn pointed toward the smaller number.
The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.
p ≠ q means that p is not equal to q
p < q means that p is less than q
p > q means that p is greater than q
p ≤ q means that p is less than or equal to q
p ≥ q means that p is greater than or equal to q.
Given, inequality
8x - 5x ≤ -6
3x ≤ -6
x≤ -6/3
x≤ -2.
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the option a is the correct option.
5. (x+3)(x-3)+(x-3)²
Simplify the expression above in standard form.
Answer: 2x^2 -6x
Step-by-step explanation:
First you should distribute the x's as shown:
(x)(x)+(x)(−3)+(3)(x)+(3)(−3)+x2+−6x+9=x2+−3x+3x+−9+x2+−6x+9
Then combine Like terms:
↓x2+−3x+3x+−9+x2+−6x+9=↓
↓(x2+x2)+(−3x+3x+−6x)+(−9+9)↓
2x2+−6x
Hope this helped... :)
What is the equation of the line in slope-intercept form?
Answer:
4x+3y=12
Step-by-step explanation:
y=mx+b
m=-4/3,b=4
y=mx+b
y=-4/3x+4
3(y=-4/3x+4)
3y=-4x+12
4x+3y=12
please rate it,thanks.
Tank B is 60% full of water. It requires an additional 2800 litres of water to be full. How many litres of water fills tank B?
subtract 2w+4 from 2w-6 show your work
Answer:
10
Step-by-step explanation:
(2w + 4) - (2w - 6)
2w + 4 - 2w + 6
2w - 2w + 4 + 6
10
I hope this helps!
Find the diagonal of a rectangle with sides 7 in and 24 in
You can use the hypotenuse formula, e.g., from the Pythagorean theorem calculator, to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w², and now you should know how to find the diagonal of a rectangle explicit formula - just take a square root: d = √ (l² + w²).
A cell phone provider offers a plan that costs 40$ per month plus 0.10$ per text message sent or received. A comparable plan costs 50$ per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each month?
In order for the plans to cost the same,
enter your response here text messages would have to be sent or received.
(Simplify your answer. Type an integer or a decimal.)
answer:
100 text messages.
$50-$40 = $10
$10/$0.1 = 100
100 text messages
the p-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. we conclude that this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 what type of error is possible here?
The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.
What is Type 1 error and Type 2 error?When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.
When we feel to reject a false H₀ it is known as type 2 error.
H₀:P= 0.12
Hₐ:P= 0.12
The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.
Therefore, it only suggests that there is a possibility that we will make a type 1 error.
Consequently, Type 1 error is the response to our query.
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(a) Annie and Dermot share $600 in the ratio 11:9.
(i) Show that Annie receives $330.
Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
As given in the question,
Total amount share by Annie and Dermot is $600.
Ratio of amount share by Annie and Dermot is 11 : 9
Let x be the amount of money.
11x + 9x = $600
⇒ 20x = $600
⇒20x/20 = $600/20
⇒x= $30
Amount received by Annie is equal to
= 11 × 30
= $330
Amount received by Dermot is equal to
= 9 × 30
= $270
Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
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An athlete ran a total of 1,500 kilometer in race before retiring. The athlete finihed thirty-two 15-kilometer race. The ret were 10-kilometer race. How many of the race were 10-kilometer race?
The number of races that were 10-kilometer long is 102.
An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.
Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.
32×15 + 10x = 1,500
480 + 10x = 1,500
10x = 1,500 - 480
10x = 1,020
x = 1,020/10
x = 102
Hence, the number of races that were 10-kilometer long is 102.
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what is the perimeter of a square if it's area is 81mm ²
Answer:
36 mm
Step-by-step explanation:
from the area we find the side by taking the square root, having found the side we multiply it by 4 and we have the perimeter, we can solve it with a simple expression that summarizes what I wrote
4√81 =
4 × 9 =
36 mm
For a ride on a rental scooter, Eric paid an $8 fee to start the scooter plus 6 cents per minute of the ride. The total bill for Eric's ride was $17.84. For how many
minutes did Eric ride the scooter?
minutes
Answer:
164 minutes
Step-by-step explanation:
$8 + $0.06m = $17.84
To isolate the m, first bring the eight to the other side
0.06m = 9.84
then divide both sides by 0.06
m = 164
3. The mean of five positive numbers is 4. When another number is added, the mean becomes 8. Find the number added.
the answer
Answer:
28
Step-by-step explanation:
mean is when you add all the numbers divide it by the amount of terms
So to find the sum of the terms we just multiply 5 by 4
20 is the sum and since the mean is 8 with 6 terms we multiply those also
8x6
48 and to find the number we subtract 48 by 20
48-20
28
Hopes this helps please mark brainliest