Given :
54% of the items are dairy products.
In ACDE, mZC = (4x – 16), m D = (6x - 1)", and mZE = (4x - 13). Find mZC.
Explanation:
We can do a diagram of triangle CDE:
The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:
[tex]\begin{gathered} m\angle C+m\angle D+m\angle E=180º \\ (4x-16)+(6x-1)+(4x-13)=180 \\ (4x+6x+4x)+(-16-1-13)=180 \\ 14x-30=180 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 14x=180+30 \\ 14x=210 \\ x=\frac{210}{14} \\ x=15 \end{gathered}[/tex]And with x = 15, replace into the expression for the measure of angle C to find it:
[tex]m\angle C=4x-16=4\cdot15-16=60-16=44º[/tex]Answer:
m
We want to solve the following system of equations.x^2 + y^2 = 1y = 2x + 2One of the solutions to this system is (-1,0).Find the other solution.
Answer:
(-3/5, 4/5)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=1 \\ y=2x+2 \end{gathered}[/tex]First, we substitute y=2x+2 into the first equation to obtain:
[tex]\begin{gathered} x^2+(2x+2)^2=1 \\ x^2+(2x+2)(2x+2)=1 \\ x^2+4x^2+4x+4x+4=1 \\ 5x^2+8x+4-1=0 \\ 5x^2+8x+3=0 \end{gathered}[/tex]We solve the derived quadratic equation for x,
[tex]\begin{gathered} 5x^2+8x+3=0 \\ 5x^2+5x+3x+3=0 \\ 5x(x+1)+3(x+1)=0 \\ (5x+3)(x+1)=0 \\ 5x+3=0\text{ or }x+1=0 \\ x=-\frac{3}{5}\text{ or -1} \end{gathered}[/tex]We then solve for the corresponding values of y using any of the equations.
[tex]\begin{gathered} \text{When x=-1} \\ y=2x+2 \\ y=2(-1)+2 \\ y=0 \\ When\text{ }x=-\frac{3}{5} \\ y=2(-\frac{3}{5})+2 \\ =\frac{4}{5} \end{gathered}[/tex]Therefore, the solutions o this system are:
(-1,0) and (-3/5, 4/5).
The other solution is (-3/5, 4/5).
Use inductive reasoning to find the next number in the pattern: 1 / 3 , 2 / 4, 3 / 5, ____.
..
SOLUTION
[tex]\frac{1}{3},\frac{2}{4},\frac{3}{5},...[/tex]The sequence progresses by the addition of 1 to both numberator and denominator.
[tex]\frac{3+1}{5+1}=\frac{4}{6}[/tex]The next number is 4/6.
f(x) = 5x2 – 7(4x + 3). What is the value of f(3)?
Given the function:
[tex]f(x)=5x^2-7(4x+3)[/tex]we can find f(3) by making x = 3 and solving for the term f. In this case, we have the following:
[tex]\begin{gathered} f(3)=5(3)^2-7(4(3)+3) \\ =5(9)-7(12+3)=45-7(15)=45-105=-60 \\ \Rightarrow f(3)=-60 \end{gathered}[/tex]therefore, f(3) = -60
One thermos of hot chocolate uses 2/3 cup of cocoa powder. How many thermoses can nalli make with 3 cups of cocoa powder?
In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
see, I got an answer but my teacher showed us the websites answer and I'm confused.
First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator.
Integers include negative numbers and, positive numbers and zero. For example, these are Integers:
[tex]4,2,-3,-8[/tex]An Integer is always a Rational number, because it can be written as a fraction with denominator 1:
[tex]\frac{4}{1},\frac{2}{1},\frac{-3}{1},\text{ }\frac{-8}{1}[/tex]Then:
A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:
[tex]\frac{1}{2}[/tex]but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):
[tex]4=\frac{4}{1}[/tex]Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.
which of the following graphs represents the equation Y -4 equals 3(x-1)?
Answer:
Explanation:
Given the equation:
[tex]y-4=3(x-1)[/tex]To determine its graph, check the graph that corresponds to the x and y-intercepts of this line.
When x=0
[tex]undefined[/tex]The area of the parallelogram below is square meters. 9 m 7 m 2m
Answer:
63 square meter
Explanation:
Area of the parallelogram = Base * Height
From the given diagram;
Base = 9m
Height = 7m
Area of the parallelogram = 9m * 7m
Area of the parallelogram = 63 square meter
Question 2You buy a house for $299,000. If you make a 20% down payment, how much will your principal and interest payment be per month if you take out a 30 year loan with an interest rate of 4.25%.
The price of the house is $29900
At first you paid 20% of that price, to calculate how much the down payment was you have to do as follows:
[tex]299000\cdot0.2=59800[/tex]The down payment was $59800 and there are $299000-$59800=$239200 left to pay.
From this $239200 you have to calculate the interest rate:
$239200*0.0425= $10166 → this represents the total interest rate you'll pay
This is a 30 year loan, which means you'll pay
30*12=360
for 360 months
Divide the principal payment $239200 by 360 to calculate the monthly fee:
[tex]\frac{239200}{360}=664.44[/tex]Do the same with the total interest rate:
[tex]\frac{10166}{360}=28.24[/tex]Monthly you'll pay $664.44 plus $28.24 of interest, that adds up for a total of $692.68
hello, i was wondering how to solve this? i am having trouble to solve this.
see the attached figure to better understand the problem
the angle between the two vectors is x and the vertex is R
Suppose you ride your bicycle to the library traveling at .50 km/min. It takes you 25minutes to get to the library. How far did you travel
Answer:
50km
Step-by-step explanation:
We know that every minute we travel .5 km....
[tex]\frac{1 min}{.50 km}[/tex]
But we want to know how far we traveled in 25 mins
[tex]\frac{25 mins}{? km}[/tex]
So we go and do....
[tex]\frac{1 min}{.50 km} * \frac{25 mins}{? km}[/tex]
Then we have to divide 25 by .50
[tex]\frac{25 mins}{.50 km}[/tex]
Which Gives us
50 so he traveled 50km
Answer:
12.5km
Step-by-step explanation:
Hey! Let's help you with your question here!
We can begin by figuring out what we know!
Known InformationBicycle traveling at .50km/min (0.50km/min)It takes 25 minutes to get to the library.What we don't know and solving for itWhat we don't know is the distance traveled based on the given time. Now, what do we do? Well, we already know that the bicycle is traveling at a distance of .50km per minute and it takes us 25 minutes to get to the library. All we need to do here is take the distance per minute and multiply it by the total amount of minutes it takes to reach the destination. It would look something like this:
[tex]=(0.50km/s)*25[/tex]
[tex]=0.50*25[/tex]
[tex]=12.5[/tex]
Therefore, we can see that if we travel at a distance of .50km/min for 25 total minutes, we get a final distance of 12.5km.
For what value of x does f(x) = 1?
Answer Choices:
A. x = 0
B. x= 1
C. x = 5
D. x = -5
Construct a 95% confidence interval of the population proportion using the given information x=180, n = 300 the lower bound is the upper bound isRound to three decimal places as needed
Given;
[tex]x=180,n=300[/tex]Then, we can find the point estimation as;
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{180}{360}=0.60 \end{gathered}[/tex][tex]Z_{\frac{\alpha}{2}}=Z_{0.05}=1.96[/tex]Thus, the margin of error E is;
[tex]\begin{gathered} E=Z_{\frac{\alpha}{2}}\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}} \\ E=1.96\sqrt[]{\frac{0.60(0.40)}{300}} \\ E=1.96\sqrt[]{0.0008} \\ E=0.055 \end{gathered}[/tex]A 95% confidence interval for population proportion p is;
[tex]\hat{p}\pm E=0.60\pm0.055[/tex]The lower bound is;
[tex]0.60-0.055=0.545[/tex]The upper bound is;
[tex]0.60+0.055=0.655[/tex]Find -7/8 - 2 1/6. Write your answer as a mixed number in simplest form.
Answer:
3 1/24
Step-by-step explanation:
1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1.2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5?3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel.(Needs exterior angles)4. Is the bottom shelf parallel to the top shelf? Explain.5. Is the bottom shelf parallel to the middle shelf? Explain.
1.
The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:
[tex]m\angle2+m\angle1=180\degree[/tex]We know the value of m∠2. Thus, we can replace it and solve for m∠1:
[tex]120\degree+m\angle1=180\degree[/tex][tex]m\angle1=180\degree-120\degree[/tex][tex]m\angle1=60\degree[/tex]2.
If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.
3.
When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:
[tex]m\angle1=m\angle5=60\degree[/tex]Then we can say that the top and middle shelves are parallel.
4.
As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.
5.
Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.
(statistics) urgently need help with question 32, is it valid or not valid & is the argument sound or not?
From the Venn diagram shown above we notice that the conclusion is false. This comes from the fact that even if all queens are women not all women are quenss.
In NOP, PNOP and m2O = 32. Find m P.
Solving Angle Problems.
[tex]PN\cong\text{ OP implies congruency, that is, length PN is the same as length OP.}[/tex]It follows therefore that
[tex]\begin{gathered} \angle NPO=\angle NOP=32^o\ldots.(\operatorname{Re}ason\colon\text{ Base angles of the isosceles triangle)} \\ \text{Hence}, \\ m\angle P=32^o \end{gathered}[/tex]The correct answer is the measure of angle P is 32 degrees
The board of directors of a company must have select a president, a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board
Given
Total number of members = 22
Find
Possible ways of selection of president, a secretary and a treasurer
Explanation
As we know , the number of possible ways of selection is given by
[tex]N=^nP_r[/tex]there are three members required so , r = 3
now , substitute the values in above equation
[tex]\begin{gathered} N=^{22}P_3 \\ N=\frac{22!}{(22-3)!} \\ \\ N=\frac{22!}{19!} \\ \\ N=22\times21\times20 \\ N=9240 \end{gathered}[/tex]Final Answer
Possible ways of selection of president, a secretary and a treasurer = 9240
a cube has 6 faces that are red, yellow, or blue. maggie rolls the cube 20 times and records the color facing up.
From the information given, the number of outcomes from 20 trials are
Red = 7
Yellow = 6
Blue = 7
From the outcomes, since the number of outcomes for red and blue are equal, it means that the number of red and blue faces would be the same. The only option where they are the same is the last option. Since the total number of faces is 6, the remaining face which is yellow is possibly 2. Thus, the correct option is
The cube has 2 red faces, 2 blue faces and 2 yellow faces
Jalen measured a bookcase to be 8.4 ft the actual measurement is 5.6 ft what is Gary percent error
We start by calculating the difference between the expected measured value and the value measured by Gary:
8.4 ft - 5.6 ft = 2.8 ft
Now we estimate what 2.8 ft is of the actual measurement 8.4 ft. That is:
2.8 / 8.4 = 0.33333... this is written in percent form as: 33.33%
This is the percent error.
What is the measurement of DC? How do you know ?
The vertices B, C and D form a right triangle.
Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.
[tex]DC^2+BC^2=BD^2[/tex]Replacing with the values, we can calculate DC:
[tex]\begin{gathered} DC^2+60^2=100^2 \\ DC^2+3600=10000 \\ DC^2=10000-3600 \\ DC^2=6400 \\ DC=\sqrt[]{6400} \\ DC=80 \end{gathered}[/tex]Answer:
The correct options are
A: 80
B: Pythagorean theorem
A card is selected from a standard deck of cards. What is the probability of selecting a King or an even card?
Given:
A card is selected from a standard deck of cards.
Required:
We need to find the probability of selecting a King or an even card.
Explanation:
The sample space =the total number of cards = 52.
[tex]n(S)=52[/tex]Let A be an event of selection a king.
The number of cards that is king = 4.
The favourable outcomes =The number of the card king
[tex]n(A)=4[/tex]The probability of selecting a king
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{4}{52}[/tex]Let B be an event of selection an even card.
There are 5 even values (2,4,6,8,10) and 4 of each in the deck.
The number of cards that is even card=20.
The favourable outcomes =The number of the even card
[tex]n(B)=20[/tex]The probability of selecting an even card
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{20}{52}[/tex]
The probability of selecting a King or an even card is
[tex]=P(A)+P(B)[/tex][tex]=\frac{4}{52}+\frac{20}{52}=\frac{24}{52}[/tex][tex]=\frac{6}{13}[/tex]Final answer:
The probability of selecting a King or an even card 6/13.
What is the sum of 7/8 and 11/8
Use diagram to find the following 1. m angle RVS = 2. M angle TVU =
The pie chart provides the following information;
[tex]\begin{gathered} m\angle RVS=(10x-10)^o \\ m\angle RVU=(8x-14)^o \\ m\angle UVT=8x^o \\ m\angle TVS=(5x+12)^o \end{gathered}[/tex]The sum of angles in a circle is 360 degrees.
Thus, we have;
[tex]\begin{gathered} (10x-10)^o+(8x-14)^o+8x^o+(5x+12)^o=360^o \\ 31x^o-12^o=360^o \\ 31x^o=360^o+12^o \\ 31x^o=372^o \\ x^o=\frac{372^o}{31} \\ x^o=12^o \end{gathered}[/tex]Then;
(a)
[tex]\begin{gathered} m\angle RVS=(10x-10)^o_{} \\ m\angle RVS=10(12)-10 \\ m\angle RVS=110^o \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle TVU=8x^o \\ m\angle TVU=8(12) \\ m\angle TVU=96^o \end{gathered}[/tex]solve the equation -8y + 8 = 37y - 7
you must first get the variables on the same side of the equal sign. It yields,
[tex]-8y-37y+8=-7[/tex]if we also pass the constant 8 to the right hand side, we have
[tex]-8y-37y=-7-8[/tex]Hence, the left and right hand sides are equal to
[tex]-45y=-15[/tex]hence, we have
[tex]y=\frac{-15}{-45}[/tex]since minus times minus is plus, we obtain
[tex]y=\frac{15}{45}[/tex]and it can be reduced to
[tex]\begin{gathered} y=\frac{15}{15\cdot3} \\ y=\frac{1}{3} \end{gathered}[/tex]Finally, the answer is
[tex]y=\frac{1}{3}[/tex]Answer:
y= 1/3
Step-by-step explanation:
Points EGNK or midpoints explain how you know figure EGHK is a parallelogram
Solution
Given a triangle FDH with E, G and H the midpoints of the sides of the triangle
Considering the figure EGHK,
Line EG is parallel and equal to line KH
Line, EK is parallel and equal to line GH
This is a feature of a parallelogram i.e two pair of opposite sides of a parallelogram are parallel and equal
∠GEK is equal to ∠GHK and ∠EGH is equal to ∠EKH
This is a feature of a parallelogram i.e
Identify the slope and the y-intercept of each line and use them to write an equation of the graph
Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:
[tex]\begin{gathered} y-\text{intercept: (0,1)} \\ \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-1-0}{3-0}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]now we can find the equation of the line using the slope and the y-intercept:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-\frac{1}{3}(x-0) \\ \Rightarrow y=-\frac{1}{3}x+1 \end{gathered}[/tex]therefore, the equation of the line is y=-1/3x+1
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. Snowfall Summary 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Number of inches (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
a)
The minimum happens at the end of the left whisker of the box plot, from the graph we notice that his happens at five. Therefore, the minium amount of snow in any of the cities was 5.
b)
The data is more concenrtated in the second quarter (from the median to the third quartile) this comes from the fact that the length of this part of the block is smaller compared to the second quarter.
c)
The data is more spread out in the second quarter (from the second quartile to the median); this comes from the fact that the length of that part of the box is larger than any other part of the plot
A data set consists of these points: (2, 4), (4, 7), (5, 12). Malinda found theregression equation to be ŷ = -2.5x - 1.5. Is she correct?A. No. The value for b is incorrect.B. Yes. This is the correct equation.OC. No. Both a and b are incorrect.D. No. The value for a is incorrect.
From the given cooridnate values, we can see that the linear regression model is given by:
the line
[tex]y=2.5x-1.5[/tex]If a and b denote the slope and y-intercept then , by comparing with the given solution, we can note that the slope (a) is incorrect. It must be 2.5 instead of -2.5. Therefore, the answer is option D
From the table above what is the probability that the respondent chosen at random answers something other than somewhat likely
Find the probability that the respondent will choose "somewhat likely". Divide the number of respondents who chose the option by the total number of respondents.
[tex]\begin{gathered} P(SL)=\frac{290}{\~likely)=\frac{290}{210+290+340+80+80}} \\ =\frac{290}{1000} \\ =0.29 \end{gathered}[/tex]Since we need to find the probability of the complement of "somewhat likely", subtract the obtained probability from 1.
[tex]\begin{gathered} P(notSL)_{}=1-0.29 \\ =0.71 \end{gathered}[/tex]