A chocolate factory has a goal to produce10121012pounds of chocolate frogs per day. If the machines operate for712712hours per day making215215pounds of chocolate frogs per hour, will the chocolate factory make it’s goal?The chocolate factory meet their goal with the total being10121012pounds of chocolate frogs produced.
Answers
First, rewrite all the mixed fractions as impropper fractions:
[tex]\begin{gathered} 10\frac{1}{2}=10\times\frac{2}{2}+\frac{1}{2}=\frac{20}{2}+\frac{1}{2}=\frac{21}{2} \\ \\ 7\frac{1}{2}=7\times\frac{2}{2}+\frac{1}{2}=\frac{14}{2}+\frac{1}{2}=\frac{15}{2} \\ \\ 2\frac{1}{5}=2\times\frac{5}{5}+\frac{1}{5}=\frac{10}{5}+\frac{1}{5}=\frac{11}{5} \end{gathered}[/tex]Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:
[tex]7\frac{1}{2}\times2\frac{1}{5}=\frac{15}{2}\times\frac{11}{5}=\frac{15\times11}{2\times5}=\frac{3\times11}{2}=\frac{33}{2}=16\frac{1}{2}[/tex]Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.
Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.
Related Questions
A pair of jeans is on sale for $30. If this price represents a 20% discount from the original price, what is the original price to the nearest cent ?
Answers
Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
Find 2 given that =−4/5 and < < 3/2
Answers
Find 2 given that =
−4/5 and < < 3/2
we know that
sin(2x) = 2 sin(x) cos(x)
so
step 1
Find the value of cos(x)
Remember that
[tex]\sin ^2(x)+\cos ^2(x)=1^{}[/tex]we have
sin(x)=-4/5
The angle x lies on III quadrant
that means
cos(x) is negative
substitute the value of sin(x)
[tex]\begin{gathered} (-\frac{4}{5})^2+\cos ^2(x)=1^{} \\ \\ \frac{16}{25}+\cos ^2(x)=1^{} \\ \\ \cos ^2(x)=1-\frac{16}{25} \\ \cos ^2(x)=\frac{9}{25} \\ \cos (x)=-\frac{3}{5} \end{gathered}[/tex]step 2
Find the value of sin(2x)
sin(2x) = 2 sin(x) cos(x)
we have
sin(x)=-4/5
cos(x)=-3/5
substitute
sin(2x)=2(-4/5)(-3/5)
sin(2x)=24/25im taking geometry A and i have a hard time with the keeping the properties straight in mathematical reasoning. the question im struggling with at the moment is in the picture here:thank you for your time
Answers
The given proposition is
[tex]m\angle UJN=m\angle EJN\rightarrow m\angle UJN+m\angle YJN=m\angle EJN+m\angle YJN[/tex]As you can observe, it was added angle YJN to the equation on both sides. The property that allows us to do that it's call addition property of equalities.
Therefore, the right answer is "addition property".Find the slope of the line passing through points -8, 8 and 7,8
Answers
We can calculate the slope of a line using the formula
[tex]m=\frac{y_b-y_a_{}}{x_b-x_a}[/tex]Let's say that
[tex]\begin{gathered} A=(-8,8) \\ B=(7,8) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} x_a=-8,y_a=8 \\ x_b=7,y_b=8 \end{gathered}[/tex]Using the formula
[tex]m=\frac{y_b-y_a}{x_b-x_a}=\frac{8-8}{7-(-8)}=\frac{0}{15}=0[/tex]The slope of the line passing through points (-8, 8) and (7,8) is 0. Which means it's a constant function (horizontal line).
What is the volume of this cone round to the nearest hundreth
Answers
We have to calculate the volume of the cone.
The volume of the cone is 1/3 of the area of the base times the height.
As the base has diameter D = 16 yd, we can calculate the area of the base as:
[tex]\begin{gathered} A_b=\frac{\pi D^2}{4} \\ A_b\approx\frac{3.14*16^2}{4} \\ A_b\approx\frac{3.14*256}{4} \\ A_b\approx200.96 \end{gathered}[/tex]Knowing the height is h = 14 yd, we then can calculate the volume as:
[tex]\begin{gathered} V=\frac{1}{3}A_bh \\ V=\frac{1}{3}*200.96*14 \\ V\approx937.81 \end{gathered}[/tex]Answer: the volume is 937.81 cubic yards.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (-6, -6); y=-2x+4
Answers
Answer:
y = 2x + 6
Step-by-step explanation:
Parallel lines have the same slope, so the slope is 2.
y = mx + b
When need the slope which is given to be 2
We will use the point given (-6,-6) for an x and y on the line
m= 2
x -= -6
y = -6
y=mx+ b
-6 = 2(-6) + b Sole for b
-6 = -12 + b Add 12 to both sides
6 = b
y = 2x + 6
Which of the following shows a matrix and its inverse?
Answers
To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be the inverse matrix.
[tex]\mleft[\begin{array}{cc|cc}-2 & 1 & 1 & 0 \\ 0 & -3 & 0 & 1\end{array}\mright][/tex][tex]\begin{gathered} R_1=\frac{R_{1}}{2}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & -3 & 0 & 1\end{array}\mright] \\ R_2=\frac{R_{2}}{3}\mleft[\begin{array}{cc|cc}1 & -\frac{1}{2} & \frac{1}{2} & 0 \\ 0 & 1 & 0 & -\frac{1}{3}\end{array}\mright] \\ R_1=R_1+\frac{R_{2}}{2}\mleft[\begin{array}{cc|cc}1 & 0 & \frac{1}{2} & \frac{1}{6} \\ 0 & 1 & 0 & \frac{1}{3}\end{array}\mright] \end{gathered}[/tex]These corresponds to:
[tex]\mleft[\begin{array}{cc}2 & -1 \\ 0 & 3\end{array}\mright]\mleft[\begin{array}{cc}\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3}\end{array}\mright][/tex]Determine if the 2 lines are parallel, perpendicular, or neither based on their slope- intercept equations.
Equations of lines H & I;
Line H: y=z
Line I: y=-7z - 33
O Not Enough Information
O Perpendicular
O Neither
POSSIBLE PO
O Parallel
Answers
Equations of lines H & I; Line H: y=z Line I: y=-7z - 33 is Perpendicular. The lines are not parallel if the slopes differ. Perpendicular lines do meet, but parallel lines do not.
How can you demonstrate that two lines in an equation are parallel?Only if the slopes of two lines are equal can they be said to be parallel. The conventional version of the equation is 2x - 3y = 4. Since a line with the equation Ax + By = C typically has a slope of -A/B, line q must have a slope of -2/-3 = 2/3.
Their equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different.
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15. [-/1 Points]DETAILSCURRENMEDMATH11 2.9.027.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.180,000120,000eBook16. [-/1 Points]DETAILSCURRENMEDMATH11 2.3.028.Divide the fraction. Express your answer to the nearest tenth. A calculator may be used.0.110.08eBook
Answers
You have the following fraction:
180000/120000
First of all you cancel zeros:
180000/120000 = 18/12
next, you can simplify
18/12 = 9/6 = 3/2
finally 3/2 is:
3/2 = 1.5
Hence: 180000/120000 = 1.5
Furthermore, for the following fraction:
0.11/0.08
Here, you can use a calculator. The result is:
0.11/0.08 = 1.375
that is approximately
1.375 ≈ 1.4
For other fractions:
350/10,000 = 35/1,000 = 0.035
which is approximately
0.035 ≈ 0.04
6.01/7.2 = 0.834 ≈ 0.83
Solve |x4|+6 = 13.
O A. x
11 and x = -11
OB. x = 11 and x = -3
OC. x = -11 and x = -3
OD. x = -11 and x = 3
Answers
Answer:
B
Step-by-step explanation:
| x - 4 | + 6 = 13
x - 4 + 6 = 13
x = 11
Or
4 - x + 6 = 13
x = -3
a^2 - b^4 Evaluate is a= -5 and b= 2
Answers
21
Explanations:Given the expression
[tex]a^2-b^4[/tex]We are to find the resulting value given that a = -5 and b = 2
[tex]\begin{gathered} =(-5)^2-(2)^2 \\ =25-4 \\ =21 \end{gathered}[/tex]Hence the value of the expression if a = -5 and b = 2 is 21
An emperor penguin has
76,634 feathers. The penguin has about 27 times as many feathers as a blue jay.
About how many feathers does the blue jay have?
Answers
Answer:
2,842 feathers
Step-by-step explanation:
An emperor penguin has 76,634 feathers. The penguin has about 27 times as many feathers as a blue jay. About how many feathers does the blue jay have?
76,634/27 = 2,842 feathers
Domain and range from the graph of a quadratic function
Answers
Given the graph of the quadratic function with vertex (-4,-3) as shown below:
The domain of the function is a set of input values. The range of a quadratic function continues in either direction along the x-axis, as shown by the arrows in the above plot. The range is the set of output values. In other words, it is the possible values of y in a quadratic function.
Thus, the domain of the function is:
[tex](-\infty,\text{ }\infty)[/tex]The range of the function is :
[tex]\lbrack-3,\text{ }\infty)[/tex]What is eight plus four minus three equal?
Answers
Answer:
9
Step-by-step explanation:
8+4-3=9
im pretty sure 8+4-3=9
a national survey of 1517 respondents reached on landlines a and cell phones found thas t the percentage of adults who favor legalized abortion has dropped from 53% a yeas r ago to 44% the study claimed that the error attributable to sampling is +5 percentage points would you claim that a majority of people are not in favor of legalized abortion. the confidence interval for the study is _% to _%
Answers
Answer:
You can claim that the majority of people are not in favor of legalized abortion.
39% < p < 49%
Explanation:
The confidence interval for the study can be calculated as:
44% - 5% < p < 44% + 5%
39% < p < 49%
Where p is the percentage of people that are in favor of legalized abortion and 5% is the error attributable to sampling.
Since the upper limit of the confidence interval is 49% (less than 50%), you can claim that a majority of people are not in favor of legalized abortion.
5) Find the volume of the cylinder whose radius is 10in and height is 20in.V-π r 2 h
Answers
determine whether the equation defines y as function of x
Answers
To answer this question, we need to solve the equation for y in the third case:
[tex]3x+2y=5\Rightarrow2y=5-3x\Rightarrow y=\frac{5}{2}-\frac{3}{2}x\Rightarrow y=-\frac{3}{2}x+\frac{5}{2}[/tex]We can see from this case that for every value of x, there must be a value in y, and this is the main condition for a relationship to be a function. Then, y is a function of x.
In the fourth case, we have a similar case, for every possible value of x, there must be a value for y. Then, y is a function of x.
As we can see, the red graph is for the linear equation and the black one is for the one with the radical ( y = -sqrt(x+1)).
If we pass a vertical line to either function (alone), we will have only a point that passes through this vertical line, and with this graphical information, we can also say that both are functions of y (for each case).
The polynomial is not written in order how many terms does the polynomial have
Answers
Answer:
[tex]\text{This polynomial has 4 terms.}[/tex]Step-by-step explanation:
a TERM is a variable, number, or product of a number and one or more variables with exponents.
Then, ordering the polynomial:
[tex]\begin{gathered} x^3+2x^2+4x-2 \\ \text{This polynomial has 4 terms.} \end{gathered}[/tex]An album received the following ratings on a 1-to-10 scale from10 music critics. What is the mean of the ratings?9.6, 9.8, 7.2, 6.4, 10.0, 8.9, 5.0, 9.8, 9.4, 6.8
Answers
Given:
The ratings are
[tex]9.6,9.8,7.2,6.4,10.0,8.9,5.0,9.8,9.4,6.8[/tex][tex]\begin{gathered} \text{Mean}=\frac{9.6+9.8+7.2+6.4+10.0+8.9+5.0+9.8+9.4+6.8}{10} \\ \text{Mean}=\frac{82.9}{10} \\ \text{Mean}=8.29 \end{gathered}[/tex]Given a Cost of $9.00 and a Percent Markup on Cost of 30% find the Selling Price.
Answers
Markup (or price spread) is the difference between the selling price of a good or service and cost. It is often expressed as a percentage over the cost.
Given:
cost = $9.00
percent markup = 30%
Let the selling price be x
The formula form percent markup is:
[tex]\text{ \% markup = }\frac{\text{ Selling price - cost}}{\cos t}\text{ }\times\text{ 100 \%}[/tex]Substituting we have;
[tex]30\text{ = }\frac{x\text{ - 9}}{9}\text{ }\times100[/tex]Solving for x:
[tex]\begin{gathered} \text{x - 9 = 2.7} \\ x\text{ = 11.7} \end{gathered}[/tex]Hence, the selling price is $11.7
Answer: $11.7
11. Natalie budgets $165 for yoga training. She buys a yoga mat for $13.25 and pays $12 per yoga class. Fill in the boxes below to write an inequality to represent the number of classes, c, that Natalie can take and stay within her budget.
Answers
She has a budget of $165, so the total cost of the yoga mat and the classes has to be equal or less than $165.
[tex]C\le165[/tex]The cost is equal to the cost of the yoga mat ($13.25) and the cost of the classes ($12*c, being c the number of classes).
We can write this as:
[tex]C=13.25+12c[/tex]We then can combine both equations and get:
[tex]13.25+12c\le165[/tex]That inequality represents that the total expenses of Natalie have to be equal or less than $165.
Answer: 13.25 + 12c <= 165
In ΔVWX, m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2. Find m∠W.
Answers
The measure of angle W in the triangle is 29 degrees
How to determine the measure of angle W?The definition of the angles are given as
m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2)
Where the triangle is given as
Triangle VWX
The sum of angles in a triangle is 180 degrees
This means that
V + W + X = 180
Substitute the known values in the above equation
So, we have
6x - 4 + x + 12 + 3x + 2 = 180
Evaluate the like terms
10x = 170
Divide by 10
x = 17
Substitute x = 17 in m∠W=(x+12)
So, we have
m∠W=(17+12)
Evaluate
m∠W = 29
Hence, the angle W is 29 degrees
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A park has several rows of trees. Each row has 5 trees. How many trees could be in the park?
Answers
Answer: so lets say x =the exact amount of rows
so each row has 5 tree's
then a is the answer
its an equation of x·5=a
so that would be a unknown number of trees so you assume that there is more than 1 row because there is several rows so its a incomplete question
Step-by-step explanation:
Consider the graph below.(3,1) (4,2) (6,3) (4,4) (8,5) Which correlation coefficient and interpretation best represent the given points?1.) 0.625, no correlation 2.) 0.791. no correlation 3.) 0.625, positive correlation4.) 0.791. positive correlation
Answers
Given the information on the problem,we have that the correlation coefficient of the data given is:
[tex]r=\frac{\sum^{}_{}(x-\bar{y})(y-\bar{x})}{\sqrt[]{SS_x\cdot SSy}}=\frac{10}{\sqrt[]{16\cdot10}}=0.79[/tex]therefore, the value of the correlation coeficient is 0.79, which shows a strong positive correlation
If f(x)3(=- Vx-3, complete the following statement:x + 2f(19) ==Answer here
Answers
This exercise is about evaluating a function at a particular argument. To do that, we replace the variable with the argument in the formula of the function, and simplify.
Let's do that:
[tex]\begin{gathered} f(19)=\frac{3}{19+2}-\sqrt[]{19-3}, \\ \\ f(19)=\frac{3}{21}-\sqrt[]{16}, \\ \\ f(19)=\frac{1}{7}-4, \\ \\ f(19)=\frac{1-28}{7}, \\ \\ f(19)=-\frac{27}{7}\text{.} \end{gathered}[/tex]Answer[tex]f(19)=-\frac{27}{7}\text{.}[/tex]The distance d (in inches) that a ladybug travels over time t(in seconds) is given by the function d (1) = t^3 - 2t + 2. Findthe average speed of the ladybug from t1 = 1 second tot2 = 3 seconds.inches/second
Answers
The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]Therefore, the correct answer is 11 inches/second.
Kacie is constructing the inscribed circle for △MNP. She constructed the angle bisectors of angle M and angle N and labeled the intersection of the bisectors as point A.Which construction is a correct next step for Kacie?Open the compass to the width of AM¯¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A M ¯ , and draw a circle centered at point , A, .Construct the perpendicular bisector of AM¯¯¯¯¯¯ .Construct the perpendicular bisector of , A M ¯ , .Open the compass to the width of AP¯¯¯¯¯ and draw a circle centered at point A.Open the compass to the width of , A P ¯ , and draw a circle centered at point , A, .Construct the line that passes through point A and is perpendicular to NP¯¯¯¯¯¯ .
Answers
From the statement, we know that:
• Kacie is constructing the inscribed circle for △MNP,
,• she constructed the angle bisectors of angle M and angle N,
• and labelled the intersection of the bisectors as point A.
(1) Now, Kacy must construct a perpendicular from the centre point to one side of the triangle.
(2) After this, she must place the compass on the centre point while adjusting its length to the point where the perpendicular crosses the triangle.
(3) Finally, she must draw the inscribed circle.
So the answer is that Kacy must construct the perpendicular bisector of AM.
AnswerConstruct the perpendicular bisector of AM
at Kelly's school, 2/3 of the play ground is covered by grass, and 3/5 of the grassy area is a baseball field. how much of the school playground is baseball feild?
Answers
At Kelly's school, 2/3 of the playground is covered by grass, and 3/5 of the grassy area is a baseball field.
How much of the school playground is the baseball field?
SOLUTION
2/3 of the playground is covered by grass and 3/5 of the grassy area is a baseball field.
The area of the school playground which is baseball field =
[tex]\frac{2}{3}\text{ x }\frac{3}{5}\text{ = }\frac{6}{15\text{ }}\text{ = }\frac{2}{5}[/tex]CONCLUSION :
[tex]\frac{2}{5}\text{ of the school field = Area of the Basket Ball Field.}[/tex]
composition of functions, interval notation
Answers
Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]What is 7050.387 rounded to the nearest ten
Answers
Hello!
When we round something to the nearest tenth, it means that the number must have just one decimal place.
Let's analyze this number and round it:
7050.387
How can we write 387 as one number?
Well, it's very close to 400, and we can "hide" these zeros.
Let's try it:
[tex]7050.387\cong7050.400\cong7050.4\cancel{00}[/tex]Answer:7050.4.
