A water park conducted a study to investigate the relationship between outdoor temperature and the number of park visitors. The correlating linear model is shown, where x represents the number of degrees over 70°F, and y represents the number of park visitors.
y= 42 + 15x
What is the correct interpretation of the y-intercept?
A.
When the temperature is 70°F, the park can expect 0 visitors.
B.
When the temperature is 70°F, the park can expect 42 visitors.
C.
When the temperature is 70°F, the park can expect 57 visitors.
D.
When the temperature is 70°F, the park can expect 15 visitors.
Answer:
b) When the temperature is 70°F, the park can expect 42 visitors.
Step-by-step explanation:
Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:
y = 42 + 15x
The general equation of a straight line plotted y against x with an intercept(c) on the y-axis and a slope(m) is given by the equation:
y = mx + c
comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.
This means that at temperature 70°F, x is 0.
therefore y = 42 + 15(0) = 42
Therefore when the temperature is 70°F, the park can expect 42 visitors.
Is (-2,-6) a solution of y < 7x +8?
Choose 1 answer:
A)Yes
B)NO
Answer:
No
Step-by-step explanation:
-6 < 7(-2) + 8
-6 < -14+8
-6 < -6
False statement
[tex]\large\text{Hey there!}[/tex]
[tex]\mathsf{y< 7x+8}[/tex]
[tex]\large\text{In order for you to see if its true or false just plug in the x and y}\\\large\text{value in your equation. Here's what I meant}\downarrow[/tex]
[tex]\mathsf{-6<7(-2)+8}\\\mathsf{7(-2)=-14}\\\mathsf{-14+8=-6}\\\mathsf{-6\neq-6}[/tex]
[tex]\boxed{\boxed{\large\text{\bf{The answer is: \boxed{\mathsf{\bf{}No,\ because\ -6\ is\ NOT\ less\ than\ -6}}}}}}\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}\notlessth[/tex]
Evan enjoys eating fresh fruits and vegetables. This
year, he decided to grow his own garden. The diagram
shows the dimensions of his garden
He fills his garden with enriched topsoil at a height of 2
inches. How much topsoil does Evan use?
48 in
cubic inches
24 in
Answer:
[tex]2304 \ in^3[/tex]
Step-by-step explanation:
Given the surface dimensions of the garden as 24 inches by 48 inches:
#Calculate surface area of the garden's top:
[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]
Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:
[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]
Hence, the amount of soil used is 2304 cubic inches.
Answer: those are right!
Hope this helps ❤️
Find the volume of a cone that has a radius of 5 centimeters and a height of 7 centimeters.
Volume = cm³
(Use 3.14 for pi and round your answer to the nearest hundredth.)
Volume of the cone is 200 cm³
Step-by-step explanation:
Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 5 inches and h = 7 inches.Volume = 1/3 × 3.14 × 5² × 7
= 183.17 in³ ≈ 200 cm³ (rounding off to nearest hundredth)
So every week in my class we do a riddle and if you’re able to solve 3 of these correctly in a row you get a prize (homework pass, money or candy etc) and this would be my 3rd one correct in a row but I want to make sure my answer is right. Please help!
Answer:
18 but look at others awnsers aswell
Step-by-step explanation:
Answer:
Their is a total of 12 rectangles in the picture
Step-by-step explanation:
All of the figures located in the picture are all rectangles
what is 9/7+5/8 as a fraction
Answer:9/7+5/8=72/56+35/56
Step-by-step explanation:9/7 times 8 by both 9 and 7 and times 7 by both 5 and 8 and you will get your answer
Answer:
[tex]1\frac{51}{56}[/tex]
Step-by-step explanation:
In order to find the answer to this question you will have to find the common denominator, (CD) multiply the denominators by the amount it takes to receive the common deliminator then do the same with the numerators without finding the common numerator, and then add the two numerators together and reduce if needed.
[tex]\frac{9}{7} +\frac{5}{8}[/tex]
Find the common denominator:
[tex]CD=56[/tex]
[tex]9\times 8 =72[/tex]
[tex]7 \times 8 = 56[/tex]
[tex]= \frac{72}{56}[/tex]
Do the same with the second fraction:
[tex]5\times7=35[/tex]
[tex]8\times7=56[/tex]
[tex]=\frac{35}{56}[/tex]
Then you would have:
[tex]\frac{72}{56} +\frac{35}{56}[/tex]
Add the numerators:
[tex]72+35=107[/tex]
[tex]=\frac{107}{56}[/tex]
Turn the improper fraction into a mixed number:
[tex]\frac{107}{56} = 1\frac{51}{56}[/tex]
You get this by dividing 107 by 56 which should give you 1 with the remainder of 51 and you keep the denominator the same.
[tex]=1\frac{51}{56}[/tex]
Hope this helps.
the area of a circle is 36/pi cm^2 What is the radius of the circle?
Answer:
the radius of the circle is 6cm
Step-by-step explanation:
the area of a circle is given to be = 36πcm²
radius of the circle = ?
to find the radius of the circle lets start by applying the formula for finding the area of a circle.
area of a circle = πr²
36πcm² = πr²
36π = πr²
divide both sides by π
36π/π = πr²/π
36 = r²
to get the value of r we are going to look for a way of getting rid of the square on "r" by squaring 36
r² = 36
r =√36
r = 6cm
therefore the radius of the circle is 6cm
Answer:
6 cm
Step-by-step explanation:
Mary delivers 32 newspapers to her costumers in 25 minutes these deliveries represent 64% of her costumers
Anna has a rectangular that is 33 inches and 75 inches. Find the perímeter of the rectangular in yards
Answer:
6 yards
Step-by-step explanation:
Perimeter of a rectangle: 2a + 2b
2(33) + 2(75)
66 + 150
216 inches
216/12 gives us feet
18/3 gives us yards
6 yards
Answer: 6 yards
a dog and a cat together weigh 27 pounds if the dog's weight is an odd number and if he weighs twice as much as she does how much do each weight.
Answer:
Dog: 9 pounds
Cat: 18 pounds
Step-by-step explanation:
x + y= 27
y = 2x
2x + x = 27
3x = 27
x = 9
y = 2x = 18
PLEASE HELP QUICK!!!!! WORTH 50 POINTS!!!!!!! Explain how to solve the equation. StartFraction c over 6 EndFraction = 9
Answer:
Solve by undoing the division by multiplying by 6 on both sides of the equation. The solution is c = 54. Check the solution by substituting 54 for the variable in the original equation and then simplify. 9 = 9 is true, so 54 is the solution.
Step-by-step explanation:
The value of c is 54.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
c/6 = 9
Solve for c.
c/6 = 9
Multiply 6 on both sides.
c = 9 x 6
c = 54
Thus,
c is 54.
Learn more about equations here:
https://brainly.com/question/17194269
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Which experssions are equivalent to 5(1/3x+7)-3(1/2x-4)?
The five-number summary for the number of accounts managed by each sales manager at Force Inc. is shown in the following table. \text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 353535 454545 505050 656565 858585 The five-number summary suggests that about 50\%50%50, percent of sales managers at Force Inc. manage fewer than what number of accounts?
The median is is the midpoint of the data. This means half is below 50 and half is above 50.
The answer would be they handle less than 50 accounts.
50% of sales managers at Force Inc. manages fewer than 50( = the median given) number of accounts.
Given that:
[tex]Min = 35\\Q_1 = 45\\Median = 50\\Q_3 = 65\\Maximum = 85[/tex]
These 5 numbers summary tells the partition of data or quartiles with endpoints as minimum and maximum.
The median is a point for which the counts of data lying above it is equal to the counts of data lying below it.
Since the question asks about :
50% Sales managers manage < ? number of accounts
and since 50% of data lie below and above the median which is 50 given in the table.
Thus we have:
50% of the Sales manager at Force Inc. managing fewer than 50(the median given) number of accounts.
Learn more here:
https://brainly.com/question/300591
Translate the phrase into an algebraic expression. 9 more than x
Answer: 9+x
Step-by-step explanation:
If you have x apples, and you need nine more, you would need to ADD 9 and "x".
please help me with this problem
Answer: The answer would be the third option 4/4 x 6 = 6
Answer:
4/4 x 6 = 6
Step-by-step explanation:
This is the answer because 4/4 is one which means 1 x 6 = 6 so they are the same.
What is the value of x?
The value of x is 8√2.
Step-by-step explanation:
From the right triangle,
The angles are 90°, 45° and the third angle is unknown.Third angle = 180° - (90°+45°) = 45°The measure of third angle is 45°The length of the side opposite to angle 45° is a=8.
Therefore, the value of y opposite to angle 45° is also 8.(b=8)
Using Pythagorean theorem,
The length of hypotenuse is c ⇒ c² = a²+b²
c² = 8²+8²
c² = 64+64 = 128
c = √128
c = √64[tex]\times[/tex]2
c = 8√2
Luna buys a shirt that costs $15.65. She gives the cashier $20 and receives $3.25 in change. What is the percent error in the amount of change she was given?
The error in the amount of change she was 25.28%.
Step-by-step explanation:
Given,
The actual price = 15.65$
The amount Luna gives to cashier = 20$
The change she receives = c = 3.25$
The actual amount of changes = x = total amount - actual price:
20$ - 15.65$ = 4.35
The percentage of error can be found using: [tex]\frac{x-c}{x}[/tex]
By putting the values in equation, we get
=> [tex]\frac{4.35 - 3.25}{4.35} * 100[/tex]
=> [tex]\frac{1.10}{4.35} * 100[/tex]
=> 25.28 %
Hence, the error in the amount of change she was 25.28%.
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
To determine the percent error in the amount of change Luna was given, we need to compare the actual change received to the correct change she should have received.
Step 1: Calculate the Correct Change
Luna gave the cashier $20 for a shirt that costs $15.65. The correct amount of change should be:
[tex]\[\text{Correct Change} = 20 - 15.65 = 4.35 \, \text{dollars}\][/tex]
Step 2: Calculate the Error
The cashier gave Luna $3.25 instead of $4.35. The error in the change given is:
[tex]\[\text{Error} = \text{Correct Change} - \text{Actual Change Given} = 4.35 - 3.25 = 1.10 \, \text{dollars}\][/tex]
Step 3: Calculate the Percent Error
Percent error is given by the formula:
[tex]\[\text{Percent Error} = \left( \frac{\text{Error}}{\text{Correct Change}} \right) \times 100\][/tex]
Substitute the values into the formula:
[tex]\[\text{Percent Error} = \left( \frac{1.10}{4.35} \right) \times 100\][/tex]
Perform the division:
[tex]\[\frac{1.10}{4.35} \approx 0.2529\][/tex]
Convert to a percentage:
[tex]\[0.2529 \times 100 \approx 25.29\%\][/tex]
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
Rationalise the denominator of 1+√2/√2
Answer:((√2) + 2)/2
Step-by-step explanation:
(1+√2)/(√2) x ((√2)/(√2))
(√2(1+√2))/2
((√2)+2)/2
Write the equation of the ellipse that has a center at
(-2, – 6), a vertex at (-8, – 6), and a covertex at
(-2, -3)
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]
Final answer:
The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).
Explanation:
The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).
The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.
Divide. Reduce the answer to lowest terms. 3/7 / 1 1/6
first off let's convert the mixed fraction to an improper fraction and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{3}{7}~~}{\frac{7}{6}}\implies \cfrac{3}{7}\cdot \cfrac{6}{7}\implies \cfrac{18}{49}[/tex]
How many liters are in 8 quarts?
Answer:
7.57082 liters
Step-by-step explanation:
2. what value of b makes the following equation true
3. which statement is true about the value of
Answer:
2. 10
3. D. 1 for all n
Step-by-step explanation:
2. The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^b = 1/a^-b
__
[tex]\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}[/tex]
The value of n is 10.
__
3. Using the above rules of exponents, the expression simplifies to ...
6^(-n+n) = 6^0 = 1
The value is 1 for any n.
The price of a pair of earrings is $22 but Priya buys them on sale for $13.20.
By how much was the price discounted?
What was the percentage of the discount?
Solution
Answer:
$8.8040%Step-by-step explanation:
The amount of the discount is the difference between the original price and the discounted price. That was ...
$22.00 -13.20 = $8.80
The percentage of the discount is the ratio of the amount of the discount to the original price. That was ...
8.80/22.00 × 100% = 40%
The price was discounted $8.80. That was a 40% discount.
Final answer:
The price of the earrings was discounted by $8.80 or 40%.
Explanation:
To find the amount by which the price was discounted, subtract the sale price ($13.20) from the original price ($22):
Discount = Original Price - Sale Price
Discount = $22 - $13.20 = $8.80
The percentage of the discount can be found by dividing the discount by the original price and multiplying by 100:
Percentage of Discount = (Discount / Original Price) * 100
Percentage of Discount = ($8.80 / $22) * 100 = 40%
Make sure to pick ALL and It needs To BE CoRRECt
Answer:
(a): 9x + 45
Option A, 9(x + 5) because it distributes into 9x + 45
Option B, 9 * x + 9 * 5 because it multiplies into 9x + 45
(b): 13 + 9y - 3 - y
Option D, 8y + 10 because it combines into this number
What is the value of x in this equation ? 5x -14 = 8x + 4
smoothie sales are on fire. the price is $3 for an adult and $1 for children. if 260 smoothies were sold for a total of 675.00 how many adults purchased smoothies? how many children?
Answer:
207.5 adult52.5 childrenStep-by-step explanation:
If "a" represents the number of adult smoothies sold, then 260-a is the number of smoothies sold to children. The total revenue is ...
3a +1(260-a) = 675
2a +260 = 675 . . . . . . eliminate parentheses
a + 130 = 337.5 . . . . . . divide by 2
a = 207.5 . . . . . . . . smoothies sold to adults
260-a = 52.5 . . . . . smoothies sold to children
_____
For the given numbers, this is the way it works out. The "half" values suggest there is a typo somewhere, possibly in the curriculum material. Talk to your teacher about this one.
Which expressions are equivalent to R16? Check all that apply.
0 (60)*
(80) •
blouse
(02)0
0 (89)16
Option C: [tex](6^{-4})^{-4}[/tex]
Option D: [tex](6^{-2})^{-8}[/tex]
Option F: [tex](6^8)^2[/tex]
Solution:
Given expression: [tex]6^{16}[/tex]
To find which expression is equivalent to the given expression.
Let us solve this using exponent rule: [tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]
Option A: [tex](6^{0})^{16}[/tex]
[tex](6^{0})^{16}=6^{0 \times 16}= 6^0[/tex]
It is not equivalent expression.
Option B: [tex](6^8)^8[/tex]
[tex](6^{8})^{8}=6^{8 \times 8}= 6^{64}[/tex]
It is not equivalent expression.
Option C: [tex](6^{-4})^{-4}[/tex]
[tex](6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option D: [tex](6^{-2})^{-8}[/tex]
[tex](6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option E: [tex](6^{-1})^{16}[/tex]
[tex](6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}[/tex]
It is not equivalent expression.
Option F: [tex](6^8)^2[/tex]
[tex](6^{8})^{2}=6^{8 \times 2}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Hence [tex](6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2[/tex] are the equivalent expressions.
Option C, Option D and Option F are correct answers.
PLEASE HELP ASAP
Thirty-two people entered the room. One-half of them decided to stay and listen to the speaker. Of those who stayed to listen, three-quarters were bored. There were
people who stayed and were not bored.
Final answer:
The question requires calculating the number of people who stayed and were not bored out of a total of 32 people.
Explanation:
The question involves calculating the number of people who stayed and were not bored out of 32 people.
Half of 32 people stayed: 32 ÷ 2 = 16 stayed.Of those who stayed, three-quarters were bored: 16 x 3/4 = 12 were bored.The number who stayed and were not bored: 16 - 12 = 4 people.Therefore, the number of people who were not bored were 4 people.
3x+4y-6z=-60
7x-5y+z=-37
2x+3y-z=-29
Answer:
{x,y,z}={-8,-3,4}
Step-by-step explanation:
NEED HELP URGENTLY ......................................................
I assumed that the unit of measure is ft.
Front+back:
S1=2×(4×3.5/2)=4×3.5=14ft²
2 sides+base:
S2=3×(9×4)=9×12=108ft²
Total area: 14+108=122ft²