Step 1 : To determine the area of the rhombus
[tex]\begin{gathered} d_1=16m,d_2\text{ = 14m } \\ Area\text{ = }\frac{1}{2}\text{ }\times d_1\text{ }\times d_2 \\ Area\text{ = }\frac{1}{2}\text{ }\times\text{ 16 }\times\text{ 14} \\ Area\text{ = }\frac{224}{2} \\ Area=112m^2 \end{gathered}[/tex]Therefore the area of the rhombus = 112m²
Solving triangles using the law of cosines . Find m
The law of cosines is defined as follows:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]For the given triangle
a=AC=8
b=AB=14
c=BC=11
∠A=∠B=?
-Replace the lengths of the sides on the expression
[tex]8^2=14^2+11^2-2\cdot14\cdot11\cdot\cos B[/tex]-Solve the exponents and the multiplication
[tex]\begin{gathered} 64=196+121-308\cos B \\ 64=317-308\cos B \end{gathered}[/tex]-Pass 317 to the left side of the expression by applying the opposite operation to both sides of it
[tex]\begin{gathered} 64-317=317-317-308\cos B \\ -253=-308\cos B \end{gathered}[/tex]-Divide both sides by -308
[tex]\begin{gathered} -\frac{253}{-308}=-\frac{308\cos B}{-308} \\ \frac{23}{28}=\cos B \end{gathered}[/tex]-Apply the inverse cosine to both sides of the expression to determine the measure of ∠B
[tex]\begin{gathered} \cos ^{-1}\frac{23}{28}=\cos ^{-1}(\cos B) \\ 34.77º=B \end{gathered}[/tex]The measure of ∠B is 34.77º
P. The Shah family basement floor is shaped like a trapezoid. The basement has sides of and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. A. What is the area, in square feet, of the basement foor? Show your work. B. What is the cost to carpet the basement floor? Explain how you found your answer
A.
In order to calculate the area of the trapezoid, we need to calculate its height:
Using the Pythagorean Theorem, we have:
[tex]\begin{gathered} 21^2=h^2+6^2 \\ 441=h^2+36 \\ h^2=441-36 \\ h^2=405 \\ h=20.12 \end{gathered}[/tex]Now, calculating the area:
[tex]\begin{gathered} A=\frac{(B+b)h}{2} \\ A=\frac{(36+24)20.12}{2} \\ A=60\cdot10.06 \\ A=603.6 \end{gathered}[/tex]B.
If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):
[tex]A=603.6\text{ ft}^2=\frac{603.6}{9}\text{ yd}^2=67.07[/tex]So the total cost is:
[tex]\text{cost}=67.07\cdot35=2347.45[/tex]So the cost is approximately $2347.45.
the prompt is in the photo
By using the given box and whisker plot, the number of students that earned a score from 77 and 90 is: N. 13.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumWhat is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot, we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 90
First quartile, Q₁ = 77
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 90 - 17
Interquartile range, IQR = 13
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(b) The area of a rectangular window is 3740 cmcm?If the length of the window is 68 cm, what is its width?Width of the windoow
Step 1
The area of a rectangle = Length x width
Step 2
Parameters given include
Area of rectangular window= 3740 square cm
Length of window = 68cm
Step 3
Substitute and solve
[tex]\begin{gathered} 3740\text{ = 68 x width} \\ \text{width = }\frac{3740}{68}\text{ = 55cm} \end{gathered}[/tex]Therefore, the width of the window = 55 cm
Gabrielle is 8 years older than Mikhail. The sum of their ages is 104. What is Mikhail's age?
Let x represent Mikhail's age.
Since Gabrielle is 8 years older than Mikhail, it means that Gabrielle's age is
x + 8
If the sum of their ages is 104, it means that
x + x + 8 = 104
2x = 104 - 8
2x = 96
x = 96/2
x = 48
Mikhail's age is 48
Yesterday Ali had n Baseball cards. Today he gave away 6. Using n, Write an expression for the number of cards Ali has left
Yesterday Ali had n Baseball cards.
Today he gave away 6 cards.
We are asked to write an expression for the number of cards Ali has left.
Ali had a total of n cards and he gave away 6 from them.
So, we have to simply subtract 6 cards from the total n cards.
[tex]n-6[/tex]Therefore, the expression is n - 6 represents the number of cards Ali has left.
I don't need Jimmy wants a game for him and his son Jimmy Jr. The game he wants is $79.93 and he only has $100 in his wallet. he found a discount for 60% off for the game. how much will he save?
Answer:
$47.96
Explanation:
The cost of the game = $79.93
He found a discount for 60% off for the game.
Therefore, the amount he will save will be:
[tex]=60\%\text{ of 79.93}[/tex]We simplify our result:
[tex]\begin{gathered} =\frac{60}{100}\times79.93 \\ =\$47.96 \end{gathered}[/tex]Jimmy will save $47.96.
Which of the following statements follows from (x - 3)2 = 7? ox2 +9=7 Ox-3=1 / OX-3 = +49 NEXT QUESTION O ASK FOR HELP
So, given the equation:
We could take the square root to both sides of the equation to obtain that:
So the correct option is B.
A restaurant serving 150 side dishes of skinless mashed potatoes each day produces two orders of mashed potatoes from each 8 ounce potato. when the skins are discarded, the potatoes have a yield percentage of 90%. However, to reduce waste and promote sales, the potato skins are instead used as an appetizer. what is the edible portion of the potato skins in ounces?
The edible portion of the potato skins in ounces is = 0.8%
What are potatoes?Potatoes are vegetable tubers that can be eaten with the skin when properly cooked.
The number of side dishes of skinless mashed potatoes= 150
Two orders of mashed potatoes = 8 ounce potato.
The potatoes with discarded skin = 90% yield
The potatoe skin= 10% of the 8 ounces
That is;
= 10/100×8
= 80/100 = 0.8 ounce
Therefore, the portion of the potatoes that consists of the skin in ounce is = 0.8 ounce
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A bookstore sells a college algebra book for $90. If the bookstore makes a profit of 25% on each sale,what does the bookstore pay the publisher for each book?
Okay, here we have this:
Considering the provided information, we obtain that:
The total price = Commission of the bookstore + Payment to the publisher
Replacing:
$90=$90(0.25)+Payment to the publisher
Payment to the publisher=$90-$90(0.25)
Payment to the publisher=$90-$22.5
Payment to the publisher=$67.5
Finally we obtain that the bookstore pay $67.5 to the publisher for each book.
If he paints 1/2 of the wall blue, hoy many square feet will be blue?
To determine how much of the wall is blue we first need to find its area. The wall is a rectangle, then its area is the product of its height and length:
[tex]\begin{gathered} A=(8\frac{2}{5})(16\frac{2}{3}) \\ A=(\frac{42}{5})(\frac{50}{3}) \\ A=(14)(10) \\ A=140 \end{gathered}[/tex]Hence, the area of the wall is 140 square ft. To determine how much of the wall is already painted we multiply this by 1/2, then:
[tex](140)(\frac{1}{2})=70[/tex]Therefore, 70 square ft are blue.
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x^2+ y^2= 5, and the path of the bean bag canbe represented by y = -0.5x^2 -1.5x + 4. To which points could she have tossed her bean bag?(-1,-2) or (-2, 1)(1.-2) or (2,1)(-1,2) or (-2,-1)(1, 2) or (2, -1)
We have two equations, the first is a circle, which we can identify by the characteristic form of the equation:
[tex]x^2+y^2=5[/tex]The second is a quadratic equation:
[tex]y=-0.5x^2-1.5x+4[/tex]We know that Sasha got the bag to land in the edge of the circle defined by the hole, equation 1.
So, to know the points at which the bag landed, we can look for th eintersection of the two equations, which is the same as solving a system of equations:
[tex]\begin{gathered} x^2+y^2=5 \\ y=-0.5x^2-1.5x+4 \end{gathered}[/tex]Since we have been given alternatives, we can check them to get the correct answer.
The first option is (-1,-2) or (-2,1). Since the sign of the alternatives are the only thing that change and the circle equation doesn't differenciate the signs, the best equation to test first is the second one. Let's try that for (-1,-2).
[tex]\begin{gathered} y=-0.5(-1)^2-1.5(-1)+4 \\ y=-0.5+1.5+4=5 \end{gathered}[/tex]We got y = 5, which is not -2, so this alternative is incorrect.
Let's got for the second alternative, (1.-2) or (2,1):
[tex]y=-0.5(1)^2-1.5\cdot1+4=2[/tex]This is also incorrect.
The third alternative is (-1,2) or (-2,-1), we already saw that for x = -1, y = 5, which makes this alternative also incorrect.
Let's check if the last one will be correct, (1, 2) or (2, -1). We already saw that for x = 1, y = 2 in the second equation, let's check if this is also correct for the first:
[tex]\begin{gathered} (1)^2+y^2=5 \\ y^2=5-1=4 \\ y=\pm2 \end{gathered}[/tex]One of the results is y = 2, so this also checks out.
The other point is (2,-1), let's check in both equations:
[tex]\begin{gathered} (2)^2+y^2=5 \\ 4+y^2=5 \\ y^2=1 \\ y=\pm1 \end{gathered}[/tex]Checks out, and:
[tex]\begin{gathered} y=-0.5(2)^2-1.5\cdot2+4 \\ y=-2-3+4=-1 \end{gathered}[/tex]And the "y" checks out too.
So, the correct alternative is the last one: (1, 2) or (2, -1).
GWhich inequalities have no solution? Check all of the boxes that apply.XX-3x -3x–4 + x>-2 + xX-2
For every number x, x = x, not x < x. So, the inequality x < x has no solution.
Since -3x = -3x for every real number, the inequality
[tex]-3x\leq-3x[/tex]holds for every real number, that is, every number is a solution.
Consider the inequality
[tex]-4+x>-2+x[/tex]Subtract x on both sides gives -4 > -2, which is not possible.
Hence the inequality - 4 + x > - 2 + x has no solution.
Consider the inequality
[tex]x-2Subtract x on both sides gives -2 < 3, which is true.Every real number is a solution of the inequality. Hence the inequality has solution.
Thus the inequalities with no solution are: x < x and -4+x>-2+x
[tex]x \geqslant - 2[/tex]
PLEASE HELP!!
A)
B)
C)
D)
Answer:
B
Step-by-step explanation:
[tex]x\geq -2[/tex] means that [tex]x[/tex] can be all values that are greater than -2, and the line under the inequality sign adds that [tex]x[/tex] can be equal to it as well.
Since B represents all values of [tex]x[/tex] that are greater than -2 along with -2 itself due to the closed circle, it is the correct answer.
Answer:
it is c i took the test i hope this helps
A brownie recipe asks for two and two thirds times as much sugar as chocolate chips. If four and one third cups of sugar is used, what quantity of chocolatechips would then be needed, according to the recipe?0308X5?
Let's call C to the cups of chocolate chips and S to the cups of sugar. We are told that the cups of sugar are 2 2/3 times the cups of chocolate, then we can formulate the following equation:
[tex]S=2\frac{2}{3}C[/tex]In the case 4 1/3 of sugar is added, we can replace 4 1/3 for S to get:
[tex]4\frac{1}{3}=2\frac{2}{3}C[/tex]By dividing both sides by 2 2/3 we get:
[tex]\begin{gathered} 4\frac{1}{3}\div2\frac{2}{3}=2\frac{2}{3}C\div2\frac{2}{3} \\ 4\frac{1}{3}\div2\frac{2}{3}=C \end{gathered}[/tex]We can rewrite the mixed fractions to get:
[tex]\begin{gathered} \frac{4\times3+1}{3}\div\frac{2\times3+2}{3}=C \\ \frac{12+1}{3}\div\frac{6+2}{3}=C \\ \frac{13}{3}\div\frac{8}{3}=C \end{gathered}[/tex]By changing the division symbol to a multiplication symbol and flipping the 8/3, we get:
[tex]\begin{gathered} \frac{13}{3}\times\frac{3}{8}=C \\ \frac{13}{8}=C \\ \frac{8+5}{8}=C \\ \frac{8}{8}+\frac{5}{8}=C \\ 1+\frac{5}{8}=C \\ 1\frac{5}{8}=C \\ C=1\frac{5}{8} \end{gathered}[/tex]Then, 1 5/8 cups of chocolate chips are needed
The table shows the number of hours spent practicingsinging each week in three samples of 10 randomlyselected chorus members.Time spent practicing singing each week (hours)Sample 1 45873 56 579 Mean = 5.9Sample 2 68 74 5 4 8 4 5 7 Mean = 5.8Sample 3 8 4 6 5 6 4 7 5 93 Mean = 5.7Which statement is most accurate based on the data?O A. A prediction based on the data is not completely reliable, becausethe means are not the same.B. A prediction based on the data is reliable, because the means ofthe samples are close together.O C. A prediction based on the data is reliable, because each samplehas 10 data points.D. A prediction based on the data is not completely reliable, becausethe means are too close together.
The means of three samples are close together. Therefore, option B is the correct answer.
In the given table 3 sample means are given.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
Here, mean of sample 1 is 5.9, mean of sample 2 is 5.8 and mean of sample 3 is 5.7.
Thus, means of these three samples are close together.
The means of three samples are close together. Therefore, option B is the correct answer.
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18. What is the probability of drawing a BLACK card with an odd number OR a card with a LETTER?A.21261B..ع1726p D. 13
Let:
A = Draw a black card
B = Draw and odd number
C = Draw a card with a letter
so:
[tex]\begin{gathered} P(A\cap B)=\frac{8}{52}=\frac{2}{13} \\ P(C)=\frac{16}{52}=\frac{4}{13} \end{gathered}[/tex]Therefore:
[tex]P((A\cap B)\cup C)=\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}[/tex]Given sin(x)=.4 and cot(x) >0 what is cos(x)?
The cotangent is given by the cosine over the sine.
If the cotangent is positive and the sine is positive, that means the cosine is also positive.
Now, in order to find the value of cos(x), we can use the following property:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (0.4)^2+\cos ^2(x)=1 \\ 0.16+\cos ^2(x)=1 \\ \cos ^2(x)=1-0.16 \\ \cos ^2(x)=0.84 \\ \cos (x)=0.917 \end{gathered}[/tex]A tree on a hillside casts a shadow c = 215 ft down the hill. If the angle of inclination of the hillside is b = 23° to the horizontal and the angle of elevation of the sun is a = 53, find the height of the tree. (Round your answer to the nearest foot.)
This is the figure, roughly. We want h.
Using smaller triangle, we can write:
[tex]\begin{gathered} \text{Cos}23=\frac{x}{215} \\ x=215\cdot\cos 23 \\ x=197.9 \end{gathered}[/tex]Also,
[tex]\begin{gathered} y=215\cdot\sin 23 \\ y=84 \end{gathered}[/tex]Now, taking the larger triangle:
The angle is 53 (30 + 23).
Let the larger side (right side) be m, which is basically:
m = h + y
Let's find m:
[tex]\begin{gathered} \tan 53=\frac{m}{x} \\ \tan 53=\frac{m}{197.9} \\ m=197.9\cdot\tan 53 \\ m=262.62 \end{gathered}[/tex]Now, we want height, h, which is:
m = h + y
262.62 = h + 84
h = 262.62 - 84
h = 178.62
Rounded to nearest feet
h = 179 feet
You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.
The given figure is a square that measures 12 foot by 12 foot. please see illustration below;
The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.
In the triangle ADC, using Pythagoras' theorem;
[tex]\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}[/tex]The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).
35+3(8-4)
(please explain how you did it)
Answer:47
Step-by-step explanation: First multiply 3x8=24 then subtract 3x4=12 from it. Which will get you 12 then add 35 to 12 which will get you 47.
35 + 3(8-4) = ?
Do the parentheses first : 8 - 4 = 4
= 35 + 3(4)
Then multiply- that's the one that is in parentheses : 3 x 4 = 12
= 35 + 12
Then just straight up add : 35 + 12 = 47
35 + 3(8-4) = 47
So ? = 47
What function makes the HIV virus unique?
The function which makes the HIV virus unique is: B. It has viral DNA that is transmitted through indirect contact with infected persons.
HIV is an acronym or abbreviation for human immunodeficiency virus and it refers to a type of venereal disease that destabilizes and destroys the immune system of an infected person, thereby, making it impossible for antigens to effectively fight pathogens.
Generally, the high mutation or replication rate of the human immunodeficiency virus (HIV) owing to its enormous genetic diversity (deoxyribonucleic acid - DNA) makes it easily transmittable from an infected person to another.
This ultimately implies that, the HIV virus is unique among other viruses because it can be transmitted without having a direct contact with an infected person such as:
Sharing a hair clipper with him or her.
Using an object that has been infected by a HIV patient.
Additionally, it is extremely difficult to develop an effective and accurate vaccine against the HIV virus because it possesses a high error rate.
Today's high temperature is 72°F. If yesterday's high temperature was 87"F, what was the change in high temperatures?
To find the change in temperature we have to do a subtraction:
Highest temperature-lowest temperature-
87-72= 15F
The change in high temperatures was 15 F .
5. Find the arclength that subtends a central angle of 175° in a circle with radius 3 feet.
As given by the question
There are given that the central angle is 175 degrees and the radius is 3 feet.
Now,
The length of an arc given it subtends a known angle at the centre is:
[tex]\text{arc length=2}\times\pi\times r\times\frac{175}{360}[/tex]Then,
[tex]\begin{gathered} \text{arc length=2}\times\pi\times r\times\frac{175}{360} \\ \text{arc length=2}\times3.14\times3\times\frac{175}{360} \\ \text{arc length=}9.16 \end{gathered}[/tex]Hence, the arclength is 9.16.
A Snack company can pack 15 granola bars in a box how many boxes are needed for 600 granola bars ?
Answer:40
Step-by-step explanation: 15 bars to a box.
600 bars in total.
600/15= 40
40 boxes of granola bars
Interpreting the whale population on the graph. I think (A).
The y-intercept is the value in the vertical axis (y-value) when the value on the horizontal axis is zero (x = 0).
Looking at the horizontal axis, the value of x indicates the generation since 2007.
That means x = 0 indicates the generation in year 2007.
The value of y for x = 0 is 240, so the population in year 2007 is 240.
Correct option: A
2) through: (-2,5), perp. to 1 = 7 1 1 LU perp m 1 2 b Sub y, m, and
Answer:
y = (-7/2)x - 2
Step-by-step explanation:
Equation of a line:
The equation of a line is given by:
y = mx + b
In which m is the slope and b is the intercept.
We want the equation of a line perpendicular to y = (2/7)x - 4.
This slope is 2/7.
When two lines are perpendicular, the multiplication of their slopes is -1.
We want to find m. So
(2/7)*m = -1
2m = -7
m = (-7/2)
So
y = (-7/2)x + b
Through the point (-2,5):
This means that when x = -2, y = 5. So
y = (-7/2)x + b
5 = (-7/2)*(-2) + b
7 + b = 5
b = 5 - 7
b = -2
So, the equation is:
y = (-7/2)x - 2
Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.Average sunset times are taken for six months across the summer. Giving the months April through September values 1 through 6, find the regression equation of the best model.y = –0.357x2 + 2.17x + 17.87y = 21.24 e0.983xy = 21.20 – 0.343xy = 20.62x–0.029
We will have the following:
From the options given we graph each possible solution with the data, that is:
In order:
From this, we can see that the function that best fits the data is:
[tex]y=-0.357x^2+2.17x+17.87[/tex]Solve the equation. f(x)=g(x) by graphing. f(x) = l x +5 l g(x) = 2x + 2 Select all possible solutions: No Solutions x=3 x=0 X=-1
As you can observe in the graph below, the given functions intercept at one point.
Hence, there is a unique solution and it's x = 3.