She will make 16 boxes.
To answer this question we simply have to divide the number of cookies (132) by the number of cookies that each box can contain.
Mathematically speaking:
[tex]132/8\text{ }[/tex][tex]16.5[/tex]Since we can´t have half boxes, we have to round the number to 16.
16 boxes.
Jamal built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box.
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will first calculate the area of the base, the area of the short side and the area of the longest side, then we have:
Base area=6 in * 14 in=84 in^2
Short side area=8 in * 6 in = 48 in^2
Longest side area=8 in * 14 in=112 in^2
Total surface area=Base area+ 2(Short side area) + 2(Longest side area)
Total surface area=84 in^2+ 2(48 in^2) + 2 (112 in^2)
Total surface area=84 in^2+ 96 in^2 + 224 in^2
Total surface area=404 in^2
Finally we obtain that the total surface area in square inches of the toy box is 404 in^2.
Please help me step by step
The value of the function f(x) at x = 0 is found as -1.
What is meant by the term function?A function is described as the connection between such a set of inputs that each have one output. A function is a relationship between inputs in which each input is linked to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x would be the input. A function's general representation is y = f(x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input has precisely one output and the output could be traced all the way back to its input.For the given question,
The graph of the function f(x) = -x² + 4x - 1 is given.
For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.
Put x = 0 in the given function.
f(0) = -0² + 40 - 1
f(0) = - 1
Thus, the value of the function f(x) at x = 0 is found as -1.
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Suppose the purr of a cat has a sound intensity that is 320 times greater than the threshold level. Find the decibel value for this cats purr. Round to the nearest decibel.
The decibel value for this cats purr round to the nearest decibel is; 25
How to calculate the decibel level?Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.
Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.
The loudness of a sound, in decibels, with intensity I is given by;
dB = 10 log₁₀(I/I₀)
We are given the intensity of a cat’s purr as I = 320I₀
Thus;
dB = 10 log₁₀(320I₀/I₀)
dB = 10 log₁₀(320)
dB = 25.05 ≈ 25
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4y - 6 = 2y + 8how to solve this equation
To solve this equation, we need to collect like terms
To collect like terms, we bring the terms similar to each other to the same side
In this case, the value having y will be brought to same side of the equation
Kindly note that if we are bringing a particular value over the equality sign, then the sign of the value has to change
This means if negative, it becomes positive and if positive, it becomes negative
Proceeding, we have
4y - 2y = 8 + 6
2y = 14
divide both sides by 2
2y/2 = 14/2
y = 7
The value of y in this equation is 7
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:A graph is titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,66, B at ordered pair 1, 110, A at ordered pair 2, 154, and the ordered pair 3, 198.Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)Part B: What are the initial value and slope of the graph, and what do they represent? (
We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).
Part A:
Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).
write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]Simplify 17(z-4x)+2(x+3z)
Answer:
23z-66x
Step-by-step explanation:
Look at the attachment please :D
Attached is a photo of my written question, thank you.
Given:
The function is,
[tex]f(x)=-2x^2-x+3[/tex]Explanation:
Determine the function for f(x + h).
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-(x+h)+3 \\ =-2(x^2+h^2+2xh)-x-h+3 \\ =-2x^2-2h^2-4xh-x-h+3 \end{gathered}[/tex]Determine the value of expression.
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-2x^2-2h^2-4xh-x-h+3-(-2x^2-x+3)}{h} \\ =\frac{-2h^2-4xh-h}{h} \\ =-2h-4x-1 \end{gathered}[/tex]So exprression after simplification is,
-2h - 4x - 1
Skis are listed by a manufacturer for $850, less trade discounts of 35% and 18%. What further rate of discount should be given to bring the net price to $446?
The Solution:
The listing price of the Skis by a manufacturer is $850.
A trade discount of 35% was allowed.
[tex]\begin{gathered} 35\text{ \% of \$850=0.35}\times850=\text{ \$297.50} \\ \text{Price}=850-297.50=\text{ \$552.50} \end{gathered}[/tex]Allowing an extra discount of 18%, we get
[tex]\begin{gathered} 18\text{ \% of \$}552.50=0.18\times552.50=\text{ \$99.45} \\ \text{Price}=552.50-99.45=\text{ \$453.05} \end{gathered}[/tex]We are required to find what further rate of discount should be given to bring the net price to $446.00
[tex]\begin{gathered} 453.05-446.00=7.05 \\ To\text{ find the required percentage of discount, we have} \\ \frac{7.05}{453.05}\times100=0.0155612\times100=1.55612\approx1.56\text{\%} \end{gathered}[/tex]Therefore, the correct answer is 1.56%
The side-by-side boxplots show consumer ratings of name brand and store brands of peanut butter.
name brands
al The median of name brands peanut butter is
grester thas the median of store
brands. (Hint* greater than or less than)
b) Approximately
% of name brands peanut butter data values are
greater than the median of the store brands peanut butter data values.
a. Median for name brands is greater than the median for store brands data values in the boxplots given.
b. Approximately 75% of the data values of name brands is greater than the median of the data values of store brands.
How to Find the Median of a Data in a Boxplot?A boxplot displays the distribution of a data such that the median is represented by the vertical line that divides the rectangular box.
25% of a data distribution is represented by the beginning of the edge of the box, while 50% is represented by the median, and 75% is represented by the point at the end of the edge of the box in the boxplot.
Therefore:
a. The median of name brands peanut butter is approximately 82-83.
The median of store brands is approximately less than 80.
Thus, we can conclude that, the median for name brands is greater than the median for store brands.
b. The median for store brands is approximately below 25% of the data values for name brands. Therefore, we would conclude that, approximately 75% of name brands data value are greater, compared to the median of the store brands data value.
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At which of the following points do the two equations f(x)=3x^2+5 and g(x)=4x+4 intersect?A. (0,5)B. (1,8)C. (0,4) D. (8,1)
Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
The sum of two numbers is 40. If 2 is added to the larger number, theresult is equal to twice the smaller number. What are the two numbers?
We have 2 numbers. We can call them x and y, being x the smaller one.
The sum of this two numbers is 40, so we can write:
[tex]x+y=40[/tex]We know that if 2 is added to the larger number (that we name as y), the result is twice the smaller number, that would be 2x. Then, we can express this as:
[tex]y+2=2x[/tex]We can express y in function of x from the second equation and then replace it in the first equation to solve for x:
[tex]y+2=2x\Rightarrow y=2x-2[/tex][tex]\begin{gathered} x+y=40 \\ x+(2x-2)=40 \\ 3x-2=40 \\ 3x=40+2 \\ 3x=42 \\ x=\frac{42}{3} \\ x=14 \end{gathered}[/tex]Now, we can calculate y as:
[tex]\begin{gathered} y=2x-2 \\ y=2(14)-2 \\ y=28-2 \\ y=26 \end{gathered}[/tex]Answer: the two numbers are 14 and 26.
The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
x + 4y = 4 2x + 4y = 8x=4y=-2
x + 4y = 4
2x + 4y = 8
x=4
y=-2
we know that
If a ordered pair is a solution of a equation, then the ordered pair must satisfy the equation
we have the ordered pair (4,-2)
Verify if the ordered pair is a solution of the given equations
Equation 1
x+4y=4
substitute the value of x and the value of y in the given equation
(4)+4(-2)=4
4-8=4
-4=4 ------> is not true
the ordered pair is not a solution of the equation
Equation 2
2x + 4y = 8
substitute the value of x and the value of y in the given equation
2(4)+4(-2)=8
8-8=8
0=8 -----> is not true
the ordered pair is not a solution of the equation
Convert: 1200 liters =kiloliters
We have from the question 1200 liters, and we need to convert it into kiloliters.
To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:
1. Find the equivalent between these two measures:
[tex]1\text{ kiloliter=}1000\text{ liters}[/tex]2. Then we have:
[tex]\begin{gathered} 1200liters*\frac{1kiloliter}{1000liters}=\frac{1200}{1000}\frac{liters}{liters}kiloliters=1.2kiloliters \\ \\ \end{gathered}[/tex]Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.
Determine the value for which the function f(u)= -9u+8/ -12u+11 in undefined
ANSWER
[tex]\frac{11}{12}[/tex]EXPLANATION
A fraction becomes undefined when its denominator is equal to 0.
Hence, the given function will be undefined when:
[tex]-12u+11=0[/tex]Solve for u:
[tex]\begin{gathered} -12u=-11 \\ u=\frac{-11}{-12} \\ u=\frac{11}{12} \end{gathered}[/tex]That is the value of u for which the function is undefined.
Hurry Will give 75 points
(Score for Question 3: of 4 points)
3. The equation y = 14x describes the amount of money Louis earns, where x is the number of hours he works
and y is the amount of money he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
Carl's Earnings
Time (h)
Money earned
($)
Hours 3 5 8 10
Money 54 90 144 180
(a) How much money does Carl earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Carl's earnings over time in hours. Remember to label the axes.
Answer:
Carl earns 18 dollars an hour, we can get this by dividing the money earned by time which gets your answer.
Part a: Carl earning per hour is $18.
Part b: More Money is earned by Carl.
Part c: The graph that represents Carl's earnings is drawn.
What is termed as the equation?A mathematical statement consisting of two expressions joined by an equal sign is known as an equation. 3x - 5 = 46 is an example of an equation. We have the value for the variable x as x = 17 after solving this equation.For the given question,
The amount of the money Louis have is defined by the equation.
y = 14xx is the number of hours.y is the amount of money.Carl's Earnings
Time (h) Hours 3 5 8 10
Money earned($) 54 90 144 180
Part a: Carl earning per hour.
For 3 hours Carl earns $54.
For one hour-$54/3 = $ 18.
Part b: More Money is earned by-
For 1 hours Carl earns $8.
For 1 hour Louis earning is y = 14×1 = $14.
Thus, Carl earns more.
Part c: The graph that represents Carl's earnings over time in hours is drawn.
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A box of a granola contains 16.8 ounces . It cost $5.19 . What is the cost , to the nearest cent , of the granola per ounce ? A . $0.12 B . $0.31 C . $3.24
The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
Choose the correct translation for the following statement.It must exceed seven.Ox<7Ox57Ox>7Ox27
Solution:
Given that a value or quantity must not exceed ten, let x represent the value or quantity.
Since it must not exceed 10, this implies that
[tex]x\leq10[/tex]The second option is the correct answer.
Determine if the proportion is true 1/6= 3/18 Proportion is not true Proportion is true
Question: Determine if the proportion is true 1/6= 3/18
Solution:
we have the following equation that it may be true or false:
[tex]\frac{1}{6}\text{ = }\frac{3}{18}[/tex]But, the above equation is equivalent to:
[tex]1\text{ x 18 = 3 x 6}[/tex]But 1x 18 = 18, and 3x 6 = 18 so the above equation is equivalent to
[tex]18\text{ = 18}[/tex]The above equality always is true, so we can conclude that the proportion is true.
LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
Find the domain of the rational function.f(x)=x−1/x+4
Given:
[tex]f(x)=\frac{x-1}{x+4}[/tex][tex]\begin{gathered} \text{Let, x+4=0} \\ x=-4 \end{gathered}[/tex]Domain:
[tex]-\infty<-4<\infty[/tex][tex](-\infty,-4)\cup(-4,\infty)[/tex]May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
cuales son los dos numeros enteros cuyo producto es 294 y cuyo cociente es 6?
1.- You need two equations
- x*y = 294
- x/y = 6
2.- Solve for x
x = 6y
(6y)y = 294
3.- Simplifying
6y^2 = 294
-Solve for y
y^2 = 294/6
What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]determine the -domain- and -range- of the graphanswer in interval notation
Explanation: Let's consider two things
- Domain = represented by the minimum and maximum x-values
- Range = represented by the minimum and maximum y-values
Step 1: Let's take a look at the picture below
As we can see above
max x-value = + ∞
min x-value = - ∞
max y-value = 4
min y-value = - ∞
Final answer: So the final answer is
[tex]\begin{gathered} \text{domain}\Rightarrow(-\infty,+\infty) \\ \text{range}\Rightarrow(-\infty,4) \end{gathered}[/tex].
What is the value of sinθ given that (3, −7) is a point on the terminal side of θ?
Solution
[tex]\begin{gathered} \text{ using pythagoras theorem} \\ \\ OB=\sqrt{OA^2+AB^2}=\sqrt{3^2+7^2}=\sqrt{58} \\ \\ \Rightarrow\sin\theta=\frac{AB}{OB}=-\frac{7}{\sqrt{58}}=-\frac{7\sqrt{58}}{58} \end{gathered}[/tex]3 1/2 berry and pinaple pies
times 2 rasberry pies
