Answers
Answer:
v ≈ 4 cm
Step-by-step explanation:
using the Sine rule in Δ VWX
[tex]\frac{v}{sinV}[/tex] = [tex]\frac{w}{sinW}[/tex]
where v = WX and w = VX
∠ W = 180° - (126 + 21)° = 180° - 147° = 33° , then
[tex]\frac{v}{sin21}[/tex] = [tex]\frac{6}{sin33}[/tex] ( cross- multiply )
v × sin33° = 6 × sin21° ( divide both sides by sin33° )
v = [tex]\frac{6sin21}{sin33}[/tex] ≈ 4 cm ( to the nearest cm )
Related Questions
A book store sells used books. Paperback books cost $1.00. Hardback books sell for $5.00. The store sold 100 books and made $260 from the sale, How many paperback books did the store sell?
Answers
ANSWER
60 paperback books
EXPLANATION
We have that:
Paperback books sell for $1.00
Hardback books sell for $5.00
The store sold 100 books and made $260.
Let the number of paperback books be x
Let the number of hardback books be y.
This means that:
x + y = 100 _____(1)
and
1 * x + 5 * y = 260
=> x + 5y = 260 ____(2)
We have two simultaneous equations:
x + y = 100 ____(1)
x + 5y = 260 ___(2)
From (1):
x = 100 - y
Put that in (2):
100 - y + 5y = 260
=> 100 + 4y = 260
Collect like terms:
4y = 260 - 100
4y = 160
y = 160 / 4
y = 40 books
This means that:
x = 100 - 40
x = 60 books
Therefore, 60 paperback books were sold.
The graph shows the number of cups of coffee Sherwin consumed in one day and the number of hours he slept that same night:A scatter plot is shown. Data points are located at 1 and 9, 3 and 5, 5 and 6, 4 and 4, 2 and 7, and 6 and 4. A line of best fit crosses the y-axis at 10 and passes through the point 6 and 4.How many hours will Sherwin most likely sleep if he consumes 9 cups of coffee? (4 points)1, because y = −x + 102, because y = −x + 109, because y = −x + 1010, because y = −x + 10
Answers
Given:
The two endpoints (1, 9) and (6, 4).
To find the number of hours will Sherwin most likely sleep if he consumes 9 cups of coffee:
Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-9}{4-9}=\frac{x-1}{6-1} \\ \frac{y-9}{-5}=\frac{x-1}{5} \\ y-9=-x+1 \\ y=-x+10 \end{gathered}[/tex]Substitute x=9 we get,
[tex]\begin{gathered} y=-9+10 \\ y=1 \end{gathered}[/tex]Hence, the answer is,
[tex]1,because\text{ y=-x+10}[/tex]Find the domain of the rational function.f(x)=(x−7)/(x+8)
Answers
Answer:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]Explanation:
Given the rational function:
[tex]f(x)=\frac{x-7}{x+8}[/tex]The domain of f(x) is the set of the values of x for which the function is defined.
A rational function is undefined when the denominator is 0.
Set the denominator of f(x) equal to 0 in order to find the value(s) of x at which f(x) is undefined.
[tex]\begin{gathered} x+8=0 \\ \implies x=-8 \end{gathered}[/tex]-8 is the excluded value of the domain.
Therefore, the domain of f(x) is:
[tex](-\infty,-8)\cup(-8,\infty)[/tex]
5. Use the equation E =- my?my where E is kinetic energy, m is the mass of an object, and v is the object'svelocityLet E = 100, 000 J and v = 24 m/s. Find the object's mass.Show your work here:Choose the correct answer:173.6 kg86.8 kg8333.3 kg347.2 kg
Answers
In general, the kinetic energy is given by the formula below
[tex]E=\frac{1}{2}mv^2[/tex]Where m is the mass and v is the speed of the object.
Therefore, in our case,
[tex]\begin{gathered} E=100000,v=24 \\ \Rightarrow100000=\frac{1}{2}m(24)^2 \end{gathered}[/tex]Solve for m as shown below
[tex]\Rightarrow m=\frac{200000}{576}=347.2222\ldots[/tex]Thus, the answer is 347.2 kg, approximately.
find the range of the data set show in the table below
Answers
Remember that
the range is the spread of your data from the lowest to the highest
so
range=Maximum value-Minimum value
we have
Maximum value=170
Minimum value=27
Range=170-27=143
therefore
answer is
Range 143For the function f(x) = x^2 + 3x,a) Find f(-2).b) Is this function linear or quadratic? Justify your answer.c) Will the graph of this function appear as a line or a parabola?
Answers
a) Evaluating the function at x= -2 we get:
[tex]f(-2)=(-2)^2+3(-2)=4-6=-2[/tex]b) Notice that the given function has the form:
[tex]y=ax^2+bx+c[/tex]Therefore f(x) is a quadratic function.
c) Since f(x) is a quadratic function its graph is a parabola.
4 The number of cars in 5 different parkinglots are listed below.35, 42, 63, 51, 74What is the mean absolute deviation ofthese listed numbers?
Answers
The number of cars in 5 different parking lots are given as data points as follows:
[tex]35\text{ , 42 , 63 , 51 , 74}[/tex]We are to determine the Mean Absolute Deviation ( MAD ). It is a statistical indicator which is used to quantify the variability of data points. We will apply the procedure of determining the ( MAD ) for the given set of data points.
Step 1: Determine the Mean of the data set
We will first determine the mean value of the data points given to us i.e the mean number of cars in a parking lot. The mean is determined by the following formula:
[tex]\mu\text{ = }\sum ^5_{i\mathop=1}\frac{x_i}{N}[/tex]Where,
[tex]\begin{gathered} \mu\colon\text{ Mean} \\ x_i\colon\text{ Number of cars in ith parking lot} \\ N\colon\text{ Total number of parking lots} \end{gathered}[/tex]We will use the above formulation to determine the mean value of the data set:
[tex]\begin{gathered} \mu\text{ = }\frac{35\text{ + 42 + 63 + 51 + 74}}{5} \\ \mu\text{ = }\frac{265}{5} \\ \textcolor{#FF7968}{\mu=}\text{\textcolor{#FF7968}{ 53}} \end{gathered}[/tex]Step 2: Determine the absolute deviation
The term absolute deviation is the difference of each point in the data set from the central tendency ( mean of the data ). We determined the mean in Step 1 for this purpose.
To determine the absolute deviation we will subtract each data point from the mean value calculated above.
[tex]AbsoluteDeviation=|x_i-\mu|[/tex]We will apply the above formulation for each data point as follows:
[tex]\begin{gathered} |\text{ 35 - 53 | , | 42 - 53 | , | 63 - 53 | , | 51 - 53 | , | 74 - 53 |} \\ |\text{ -18 | , | -11 | , | 10 | , | -2 | , | }21\text{ |} \\ \textcolor{#FF7968}{18}\text{\textcolor{#FF7968}{ , 11 , 10 , 2 , 21}} \end{gathered}[/tex]Step 3: Determine the mean of absolute deviation
The final step is determine the mean of absolute deviation of each data point calculated in step 2. Using the same formulation in Step 1 to determine mean we will determine the " Mean Absolute Deviation ( MAD ) " as follows:
[tex]\begin{gathered} \mu_{AD}\text{ = }\frac{18\text{ + 11 + 10 + 2 + 21}}{5} \\ \mu_{AD}\text{ = }\frac{62}{5} \\ \textcolor{#FF7968}{\mu_{AD}}\text{\textcolor{#FF7968}{ = 12.4}} \end{gathered}[/tex]Answer:
[tex]\textcolor{#FF7968}{MAD=12.4}\text{\textcolor{#FF7968}{ }}[/tex]I need the answer for this question on math
Answers
Answer:
12.8 grams per 1 package
102.4 grams per 8 packages
128 grams per 10 packages
Step-by-step explanation:
we can take
25.6 ÷ 2
to get the unit rate (number of grams per 1 package)
25.6 ÷ 2 = 12.8
12.8 grams per 1 package
multiply 12.8 by 8 to get the amount of grams per 8 packages
12.8 * 8 = 102.4
102.4 grams per 8 packages
we can set up a proportion to find the number of packages for 128 grams
let p = number of packages
12.8/1 = 128/p
12.8 = 128/p
multiply by "p" on both sides to get rid of the "p" in the denominator
12.8*p = (128/p )* p
12.8p = 128
divide by 12.8 on both sides to isolate "p"
12.8p = 128
÷12.8 ÷12.8
p = 10
128 grams per 10 packages
A certain type of cell doubles every 5 hours. If you started with 38 cells, how manywould you have after 15 hours? (gridded response)
Answers
First divide 15 hours by 5 :
15/5 = 3
So, we obtain that the cell will double 3 times
since the initial number o f cells is 38
5hours = 38x2 = 76
10 hours = 76x2= 152
15 hours =152 x2 = 304
304 cells
Challenge The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .
Answers
The graph shows triangle ABC with vertices as follows;
[tex]\begin{gathered} A=(-5,5) \\ B=(-2,4) \\ C=(-2,3) \end{gathered}[/tex]When translated 6 units to the right, and 7 units down, its becomes,
[tex]\begin{gathered} A^{\prime}=(1,-2) \\ B^{\prime}=(4,-3) \\ C^{\prime}=(4,-4) \end{gathered}[/tex]That means its reflected across the y-axis and the x-axis as follows;
[tex](x,y)\rightarrow(x+6,y-7)[/tex]After this the translation is complete.
Question 7. Y=(5/2)^xSketch the graph of each of the exponential functions and label three points on each graph.
Answers
Given:
[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]To sketch the graph:
First find the three points.
Put x=-1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]Put x=0 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]Put x=1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).
The graph is,
Here are the numbers of times 14 people ate out last month.7,5, 3, 6, 3, 3, 6, 5, 6, 3, 6, 5, 5,4Send data to calculatorFind the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."
Answers
Given,
The numbers of times 14 people ate out last month is,
7,5, 3, 6, 3, 3, 6, 5, 6, 3, 6, 5, 5,4
Arranging the data is ascending order,
3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
The frequency of 3, 5 and 6 is same.
The number with maximum frequency is called the mode of the data.
The mode of the data set is 3, 5, 6.
Ian is a salesperson who sells computers at an electronics store. He makes a base payof $80 each day and then is paid a $5 commission for every computer sale he makes.Make a table of values and then write an equation for P, in terms of x, representingIan's total pay on a day on which he sells x computers.
Answers
ANSWER
[tex]P=5x+80[/tex]EXPLANATION
Let the number of computers sold be x.
Let the total pay be P.
We have to find the equation that represents the total pay in terms of the number of computers sold.
The equation that represents the total pay is a linear equation and a linear equation has a general form of:
[tex]y=mx+b[/tex]where m = slope
b = y intercept
To find the slope, we have to apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two sets of points from the table.
Let us pick (0, 80) and (3, 95)
Therefore, the slope, m, is:
[tex]\begin{gathered} m=\frac{95-80}{3-0} \\ m=\frac{15}{3} \\ m=5 \end{gathered}[/tex]Now, we apply the point-slope formula to find the equation:
[tex]P-P_1=m(x-x_1)[/tex]Note: P is used in place of y (the dependent variable)
Therefore, we have:
[tex]\begin{gathered} P-80=5(x-0) \\ P-80=5x \\ \Rightarrow P=5x+80 \end{gathered}[/tex]That is the equation that represents the total pay, P.
Hi! Can someone please check my work real quick? I’m not sure what I’m doing wrong. I’m trying fo find the remainder using synthetic division.
Answers
Given:
The polynomial is given as,
[tex]\begin{gathered} p(x)=2x^3+4x^2-5 \\ g(x)=x+3 \end{gathered}[/tex]The objective is to divide the polynomial by synthetic division.
Explanation:
The general equation of a polynomial with degree 3 is,
[tex]f(x)=ax^3+bx^2+cx+d[/tex]So, consider the given polynomial as,
[tex]p(x)=2x^3+4x^2+0x-5[/tex]The divisor can be converted as,
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]To find synthetic division:
Now, the synthetic division can be evaluated as,
Hence, the remainder of the division is -23.
Solve 3x-9 = 6.A. x = 2B. x=-1C. x = 1D. x = 5
Answers
Step 1. The expression that we have is:
[tex]3x-9=6[/tex]And we need to solve for x.
If we are going to solve for x, we need to have the 'x' alone on one side of the equation.
For that, the first step is to add 9 to both sides:
[tex]3x-9+9=6+9[/tex]Step 2. On the left side, -9+9 cancel each other, and on the right side 6+9 is 15:
[tex]3x=15[/tex]Step 3. The next step is to divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3}[/tex]In this way, 3/3 on the left side cancel each other and we are left only with x:
[tex]x=\frac{15}{3}[/tex]And on the right side, 15/3 is equal to 5:
[tex]\boxed{x=5}[/tex]This is shown in option D.
Answer:
D. x=5
total of students 50 students that dont wear glasses and 12 that do what the ratio
Answers
the ratio is 6:25, because for every 25 students that dont wear glesses there are 6 that do.
Answer:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
Step-by-step explanation:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The total number of students is 62, and 12 of them wear glasses.
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The total number of students is 62, and 50 of them do not wear glasses.
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The 50 students do not wear glasses, while 12 students wear glasses.
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
There are 12 students who wear glasses and 50 who do not.
what is 100 divided by 74 rounded to the nearest 10
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
100 ÷ 74
Step 02:
Given the diagram shown, which of the following statements are true.
Answers
I,II
1) Since in this diagram we have two triangles, whose sides AI and LH are parallel to each other we can state the following:
2) And since similar triangles have congruent angles and proportional sides, we can state as true the following:
I.∠JHL ≅ ∠JIK Similar triangles have congruent angles
As they are similar triangles we can write out the following ratios:
[tex]\frac{JI}{JH}=\frac{JK}{JL}[/tex]These are true
And the third is not correct.
3) Hence, the answer is I,II
[in the following write an expression in terms of the given variables that represents the indicated quantity.]the sum of three consecutive integers if the greatest integer is x.the expression for the sum of the three consecutive integers is _________
Answers
Answer
Sum of the three consecutive integers = 3x - 3
Explanation:
Find the sum of three consecutive integers
Condition given: Greatest integer should be x
Since, x is the greatest integer, therefore, the other integers should be less than x
The three consecutive integers are: x, x - 1, and x - 2
Sum of the three integers = x + x - 1 + x - 2
Sum = x + x - 1 + x - 2
Collect the like terms
= x + x + x - 1 - 2
Sum = 3x - 3
Therefore, the sum of the three consecutive integers is 3x - 3
What is syntax? PLS HURRY
Referring to a dictionary when you are unsure of a word's meaning
The careful and purposeful choice of words to reach a desired effect
The way writers arrange words and punctuation to create sentences
Using a clue in a sentence to determine the meaning of a word
Answers
The study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
What is syntax?The study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences. Word order, grammatical relationships, hierarchical sentence structure (constituency), agreement, the nature of cross-linguistic diversity, and the connection between form and meaning are among the primary issues of syntax (semantics). There are many different approaches to syntax, each with a unique set of underlying premises and objectives.A division of grammar is syntax. The entire set of rules that make up a language, including syntax, is referred to as grammar. "Syntax skills help us comprehend how sentences work—the meanings underlying word order, structure, and punctuation. Syntax deals with the way that words are placed together to make phrases, clauses, and sentences.Therefore, the study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
Know more about syntax here:
https://brainly.com/question/831003
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Answer:
the study of syntax in linguistics focuses on how words and morphemes come together to produce longer language constructs like phrases and sentences.
Step-by-step explanation:
Draw the dilation of PQRS using center Q and scale factor 1/2. Label the dilation TUWX. 2. Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD. 3. Show that TUWX and ABCD are similar.
Answers
Based on the given image, you obtain the following figures:
Draw the dilation of PQRS using center Q and scale factor 1/2
Draw the dilation of PQRS with center R and scale factor 2. Label the dilation ABCD
You can notice that both figure TUWX and ABCD are similar because the quotient between sides TU and PQ, XW and RS, UW and BC, TX and AD are the same.
5.) figure 12.16 shows the floorplan for a modern one story house. Bob calculates the area of the floor of the housing this way: 36•72-18•18 = 2268 feet squared. what might Bob have in mind? Explain why Bob’s method is a legitimate way to calculate the floor area of the house, and explain clearly have one or both of the moving and additivity principles on area apply in this case
Answers
From the given image, the Area of the floor can be calculated by removing/subtracting the area of the two triangles from the area of the rectangle.
Area of a rectangle is;
[tex]\begin{gathered} A_r=lb \\ A_r=36.72 \end{gathered}[/tex]Area of the two triangles;
[tex]\begin{gathered} A_t=\frac{1}{2}bh+\frac{1}{2}bh=\frac{1}{2}(18.18)+\frac{1}{2}(18.18) \\ A_t=18.18 \end{gathered}[/tex]The Area of the floor is;
[tex]\begin{gathered} A=A_r-A_t \\ A=36.72-18.18 \\ A=2592-324 \\ A=2268ft^2 \end{gathered}[/tex]Find the value of x and y.
Answers
These 3 angles are equal value
5x + 1 = 6x - 10 = y
Then
5x + -6x = -10 - 1
-x = 11
x= 11
NOW find y value
y = 5x + 1
y= 6x - 10
y = 5•( 11) + 1= 56
y= 6•( 11) -10= 56
Answer is y= 56
Find the value of the test statistic z using z =P-Ppan37) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics includen = 1158 subjects with 30% saying that they play a sport.Answer: - 13.6138) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, andthe sample statistics include n = 647 drowning deaths of children with 30% of them attributable to beaches.Answer: 2.94
Answers
37. The given p-value is 0.5
Also the observed proportion is:
[tex]\hat{p}=30\%=0.3[/tex]And q is (1-p), so:
[tex]q=1-0.5=0.5[/tex]And the n-value is given 1158.
By replacing these values into the test statistic formula we obtain:
[tex]z=\frac{\hat{p}-p}{\sqrt[]{\frac{p\cdot q}{n}}}=\frac{0.3-0.5}{\sqrt[]{\frac{0.5\cdot0.5}{1158}}}=\frac{-0.2}{\sqrt[]{0.0002}}=\frac{-0.2}{0.015}=-13.61[/tex]The answer is -13.61
2. Which expression is equivalent to x⁴+6x²+9? * A. g(x)=2(x–3)²–72B. g(x)=2(x²–6x–27)C. g(x)=2(x–9)(x+3)D. g(x)=2x²–18x+6x–54
Answers
Explanation:
The best way to find the zeros of the function is to write the polynomial as a product of linear terms with the form (x - c). Therefore, the right answer is:
C. g(x) = 2(x - 9)( x + 3)
Because is written as a product and all factors are linear.
In this case, we can identify the zeros making each
9. Josie has $30 to spend at a festival. It costs $5 to enter the festival, and the game she wants to play costs $1.40. Write the inequality and use it to determine the number of games (g) that Josie can play.
Answers
She has only $30 with her.
It will cost her $5 to enter the festival and the game she wants to play cost $1.40 .
let
g = number of games
Therefore, the inequality for the number of games she can play can be represented below
[tex]\begin{gathered} 5+1.40g\leq30 \\ \text{where} \\ g=\text{ number of games she can play} \end{gathered}[/tex]The number of games she can play can be calculated below
[tex]\begin{gathered} 5+1.40g\leq30 \\ 1.40g\leq30-5 \\ 1.40g\leq25 \\ \text{divide both sides by }1.40 \\ g\leq\frac{25}{1.40} \\ g\leq17.8571428571 \\ g\leq17.86 \\ \text{she can only play approximately 17 games} \end{gathered}[/tex]Logan made 5 1/4 pounds of trail mix. If he puts 3/4 pounds into each bag how many bags can Logan fill?
Answers
Which of the following represents the equation of a quadratic curve?y = 3x + 7y = 8 - 3x + 7x2y = 7(3)xy = 8 x 6
Answers
An equation will be a quadratic curve when the expression has the following definition
[tex]y=ax^2+bx+c[/tex]We can have b and c equal to 0, but never a, therefore we have few variations like
[tex]\begin{gathered} y=ax^2+bx \\ y=ax^2+c \\ y=ax^2 \end{gathered}[/tex]All they are quadratics. Looking at the options we can see that the only function that has that definition is
[tex]y=8-3x+7x^2[/tex]Therefore the correct answer is
[tex]y=8-3x+7x^{2}[/tex]Given that sin A= -4 over 5 and angle A is in quadrant 3, what is the value of cos(2A)?
Answers
Solution:
Given;
[tex]\sin(A)=-\frac{4}{5}[/tex]Then, the value of cosine x is;
[tex]\cos(A)=-\frac{3}{5}[/tex]Because cosine and sine are negative on the third quadrant.
Then;
[tex]\begin{gathered} \cos(2A)=\cos^2(A)-\sin^2(A) \\ \\ \cos(2A)=(-\frac{3}{5})^2-(-\frac{4}{5})^2 \\ \\ \cos(2A)=\frac{9}{25}-\frac{16}{25} \\ \\ \cos(2A)=-\frac{7}{25} \end{gathered}[/tex]How much work is done when a book weighting 2.0 new newtons is carried at a constant velocity from one classroom to another classroom 26 meters away.