Triangle JKL is similar to triangle MNO. find the measure of side NO. Round your answer to the nearest tenth if necessary.
Answers
Given Data
[tex]\Delta JKL\cong\Delta MNO[/tex]From the propery of the similar triangles,
[tex]\frac{JK}{MN}=\frac{KL}{NO}=\frac{JL}{MO}[/tex]Substituting the know values in the above equation,
[tex]\begin{gathered} \frac{KL}{NO}=\frac{JL}{MO} \\ \Rightarrow\frac{8}{NO}=\frac{11}{49} \\ \Rightarrow NO=\frac{8\times49}{11} \\ \Rightarrow NO=35.63 \end{gathered}[/tex]Thus, the requried value of NO nearest to the tenth is 35.6.
Related Questions
x = ____ unitsRound your answer to the nearest tenth of a degree.
Answers
To find x, we will use the Pythagoras theorem;
opposite² + adjacent² = hypotenuse²
x² + 12² = 20²
x² + 144 =400
subtract 144 from both-side of the equation
x² = 400 - 144
x² =256
Take the square root of both-side
x = 16
Joes bakery is making 168 cupcakes for a large catering order. Their recipe calls for 5 ounces of flour for 12 cupcakes. How much flour will they need for their catering order? Enter a whole number pounds (IB) and enter the ounces ( oz ) as a number between 0 and 15, using the fact that 1 IB = 16 oz.
Answers
We have to find the amount of flour needed.
The order is 168 cupcakes.
The proportion between cupcakes and flour is: 5 ounces of flour for 12 cupcakes.
Then, we can use the rule of three to find the total amount of flour needed:
[tex]\begin{gathered} 12\text{ cupcakes}\longrightarrow5\text{ oz of flour} \\ 168\text{ cupcakes}\longrightarrow x=168\cdot\frac{5}{12}=70\text{ oz of flour} \end{gathered}[/tex]We can now express it in pounds and ounces using the fact that 1 lb = 16 oz.
We start by calculating how many pounds is 70 oz and then complete the decimal part expressed in ounces:
[tex]\begin{gathered} 70\text{ oz}\cdot\frac{1\text{ lb}}{16\text{ oz}}=4.375\text{ lb} \\ 0.375\text{ lb}\cdot\frac{16\text{ oz}}{1\text{ lb}}=6\text{ oz} \\ \Rightarrow70\text{ oz}=4\text{ lb }6\text{ oz} \end{gathered}[/tex]Answer: The amount of flour needed is 4 lb and 6 oz.
Yoko is saving money to buy a game so far she has saved $30 which is 3/5 of the total cost of the game how much does the game cost
Answers
Answer:
The game costs $50.
Step-by-step explanation:
This question can be solved using a rule of three.
$30 is 3/5 = 0.6 = 60% of the total cost x.
So
0.6x = 30
x = 30/0.6
x = 300/6
x = 50
The game costs $50.
1. Choose the item that has measurable volume.
Answers
So to meassure a volume we have to mesure the lenght, the high and the wide so in the case the item that can be messure its volume is:
Cereal Box
d. 10.614. Find the midpoint between points X (10,-5) and Y (7,-4) to the nearest tentha. (8.5, 4.5)b. (17,-9)c. (17, -9)d. (8.5, -4.5)
Answers
Answer:
d. (8.5, -4.5)
Explanation:
The coordinates of the midpoint can be calculated as:
[tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]Where (a, b) are the coordinates of the first point and (c, d) are the coordinates of the second point.
Then, replacing (a,b) by X(10, -5) and (c, d) by Y(7, -4), we get:
[tex]\begin{gathered} (\frac{10+7}{2},\frac{-5+(-4)}{2})_{} \\ (\frac{17}{2},\frac{-9}{2})_{} \\ (8.5,-4.5) \end{gathered}[/tex]Therefore, the coordinates of the midpoint are (8.5, -4.5)
Use the triangle below to solve for X.What trig function will you use to solve for X X=
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By definition, a Right triangle is a triangle that has an angle whose measure is 90 degrees (this angle is also known as "Right angle").
You can identify that the triangle given in the exercise is a Right triangle.
In order to find the value of "x", you need to use the following Trigonometric function "Cosine":
[tex]\cos \alpha=\frac{adjacent}{hypotenuse}[/tex]Because, in this case, you can identify that the side whose length is 19, is adjacent (or next to) to the angle 51°, and the hypotenuse (the longest side of the triangle) is the lenght of the side you must find.
Then, you can determine that:
[tex]\begin{gathered} \alpha=51\degree \\ adjacent=19 \\ hypotenuse=x \end{gathered}[/tex]Substituting values:
[tex]\cos (51\degree)=\frac{19}{x}[/tex]2. Solving for "x", you get:
[tex]\begin{gathered} x\cdot\cos (51\degree)=19 \\ \\ x=\frac{9}{\cos (51\degree)} \\ \\ x=14.30 \end{gathered}[/tex]The answers are:
1. Co
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Ok, and do you need to find the value of "x"?
There are 3 minutes ofcommercials for every15 minutes of television.How many minutes ofcommercials are there in1 hour and 20 minutes oftelevision?
Answers
For every 15 minutes, there are 3 minutes of commercials We can write this as
[tex]\frac{3\text{ min commerical}}{15\text{minutes}}[/tex]Now in one hour, there are 60 minutes; therefore, in 1 hour and 20 minutes, there are 60+ 20 = 80 minutes.
Let us call x the number of minutes in these 80 minutes, then we have the equation
[tex]\frac{3\text{ min commerical}}{15\text{minutes}}=\frac{x\text{ min commerical}}{80\text{minutes}}[/tex]which says that the ratio of commercial minutes and the television minutes must remain constant.
Cross multiplication gives
[tex]3\cdot80=x\cdot15[/tex][tex]\rightarrow15x=240[/tex]dividing both sides by 15 gives
[tex]x=16.[/tex]Hence, in 1 hour and 20 minutes, there are 16 minutes of commercial.
Tyrell was late for class 3 times in the month of June . Each time he was late he missed 5 and 1/2 minutes of class time . What is the total amount of class time Tyrell missed in the month of June ? A. 8 and 1/2 B . 15 minutes C . 16 and 1/2
Answers
Tyrell was late 3 times, each time he was late for 5 1/2 minutes, to determine how much time he missed in June, you have to multiply 5 1/2 by 3
[tex]5\frac{1}{2}\cdot3[/tex]First, express the mixed number as a fraction:
-Divide the whole number by 1 and add 1/2
[tex]5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}[/tex]-Multiply the first fraction by 2, to express it as its equivalent with denominator 2, and add both fractions:
[tex]\frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{10+1}{2}=\frac{11}{2}[/tex]Multiply the result by 3
[tex]\frac{11}{2}\cdot3=\frac{11}{2}\cdot\frac{3}{1}=\frac{11\cdot3}{2}=\frac{33}{2}[/tex]Express the result as a mixed fraction:
Divide 33 by 2:
[tex]33\div2=16.2[/tex]The whole number of the result is 16 and there are 0.5 remainings.
0.5 expressed as a fraction is 1/2.
So Tyrell missed 16 and 1/2 minutes in the month of June
f(x) = integrate t ^ 4 dt from 0 to x ^ 2 * then
Answers
The given function is:
[tex]f(x)=\int_0^{x^2}t^4dt[/tex]Therefore, by evaluating the integral on the right hand side, it follows that:
[tex]\begin{gathered} f(x)=\frac{t^{4+1}}{4+1}\biggr\rvert_0^{x^2} \\ f(x)=\frac{t^5}{5}\biggr\rvert_0^{x^2} \\ f(x)=\frac{(x^2)^5}{5}-\frac{(0)^5}{5} \\ f(x)=\frac{x^{10}}{5} \end{gathered}[/tex]Therefore, by differentiating with respect to x, it follows that:
[tex]\begin{gathered} f^{\prime}(x)=10\times\frac{x^{10-1}}{5} \\ f^{\prime}(x)=2x^9 \end{gathered}[/tex]Therefore,
f'(x) = 2x⁹
The equation y = ax² +bx+c goes through the coordinates (-3, -34), (5,-2), and (7,-14). What are the values of a, b, and c?
Answers
The values of a, b and c in the quadratic equation y = ax² + bx + c are a = -1, b = 6, y = -7
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the quadratic equation:
y = ax² + bx + c
At the point (-3. -34):
-34 = a(-3)² + b(-3) + c (1)
At the point (5. -2):
-2 = a(5)² + b(5) + c (2)
At the point (7, -14):
-14 = a(7)² + b(7) + c (3)
From the three equations:
a = -1, b = 6, y = -7
The values of a, b and c are a = -1, b = 6, y = -7
Find out more on equation at: https://brainly.com/question/2972832
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HELPPPPPEvaluate the equation p(x)= 4x - 2;find p(2)
Answers
Answer:
p(2) = 6
Explanation:
To find p(2), we need to replace x by 2 on the equation of p(x). So, p(2) is equal to:
[tex]\begin{gathered} p(x)=4x-2 \\ p(2)=4(2)-2 \\ p(2)=8-2 \\ p(2)=6 \end{gathered}[/tex]Therefore, the answer is p(2) = 6
For the food described, find what percent of total calories is from fat if necessary round to the nearest tenth of a percent
Answers
Given:
Total calories = 180
Calories from fat = 45
The percent of total calories from fat is given as:
[tex]\begin{gathered} =\frac{45}{180}\times100 \\ =\frac{5}{2}\times10 \\ =5\times5 \\ =25 \end{gathered}[/tex]Therefore, the percent of calories from fat is 25%
Write the expression with a single base and single positive exponent then simplify. y^{-4}(y^2)^2 The base is AnswerThe exponent is AnswerThis simplifies to Answer
Answers
The expression is given as,
[tex]y^{-4}\cdot(y^2)^2[/tex]Consider the following laws of exponents,
[tex]\begin{gathered} (x^m)^n=x^{mn} \\ x^m\cdot x^n=x^{m+n} \end{gathered}[/tex]Use the above laws to simplify the expression as follows,
[tex]\begin{gathered} =y^{-4}\cdot(y^{2\cdot2}) \\ =y^{-4}\cdot(y^4) \\ =y^{-4+4} \\ =y^0 \\ =1 \end{gathered}[/tex]The value 1 can be expressed as,
[tex]=1^1[/tex]Therefore, the base is 1, and the exponent is also 1.
GuitarPianoGirls 8113Did a larger percentage of the girlsor the boys pick piano?GirlsBoys
Answers
Answer: Larger percentage of boys pick piano
Explanation:
From the diagram, number of girls that pick piano = 12
Total number of girls = 8 + 12 = 20
∴ percentage of girls that pick piano = (number of girls that pick piano)/((total number of girls x 100
i.e )percentage of girls that pick pian = 12/20 x 100 = 60%
Similarly for boys, onumber ofboyls that pick piano =82
Total number of boys = 4 + 8 = 12
∴ percentage of boys that pick piano = (number of boys that pick piano)/(total number of boys) x 100
i.e percentage of boys that pick piano = 8/12 x 100 = 66.67%
Since 66.67% for boys is greater than 60% for girsl, then lLarger percentage of boys pick piano
The angle of depression from the top of a house to a point on the ground is x°. The distance from the point on the ground to the top of the house is 20 yards m and the house is 7 yards high......
Answers
We know the angle of depression is x, so using alternate interior angles, the angle at the ground is also x
We can either use trig functions or the Pythagorean theorem to find d
I like to use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
7^2 + d^2 = 20^2
49 + d^2 = 400
d^2 = 400-49
d^2 = 351
Taking the square root of each side
d = sqrt(351)
d =18.734994
To the nearest tenth
d = 18.7 yds
thefind the slope of the line that goes through.givonpoints (8,9) (8,1)
Answers
The formula used to calculate the slope of a line given the coordinates on the line is given to be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points:
[tex]\begin{gathered} (x_1,y_1)=(8,9) \\ (x_2,y_2)=(8,1) \end{gathered}[/tex]Therefore, we can calculate the slope to be:
[tex]\begin{gathered} m=\frac{1-9}{8-8}=\frac{-8}{0} \\ m=undefined \end{gathered}[/tex]Therefore, the slope is undefined.
I need help with this question I will attach the rest of the images.
Answers
We have that there are in total 272 people
for the first question:
[tex]\frac{50}{272}=0.1838\rightarrow18\text{ \%}[/tex]for the second question
[tex]\frac{156}{272}=0.5735\rightarrow57\text{ \%}[/tex]for the third one
[tex]\frac{66}{86}=0.7674\rightarrow77\text{ \%}[/tex]for the fourth one:
[tex]\frac{86}{272}=0.316\rightarrow31\text{ \%}[/tex]last one
[tex]\frac{50}{116}=0.43\rightarrow43\text{ \%}[/tex]Write the first five term of the sequence whose nth term is given by the rule.
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In this case, n can take 1,2,3,4 and 5. So, the first term is
[tex]a_1=\frac{1}{1+1}=\frac{1}{2}[/tex]The second term is
[tex]a_2=\frac{2}{2+1}=\frac{2}{3}[/tex]The third term is
[tex]a_3=\frac{3}{3+1}\questeq\frac{3}{4}[/tex]The fourth term is
[tex]a_4=\frac{4}{4+1}=\frac{4}{5}[/tex]and the fifth term is
[tex]a_5=\frac{5}{5+1}=\frac{5}{6}[/tex]Factor this question 16x^4-36
Answers
Based on the given that we have, we could say that
[tex]\begin{gathered} a^2=16x^4 \\ b^2=36 \\ \\ \text{Get the square root of both and we get} \\ a^2=16x^4 \\ \sqrt[]{a^2}=\sqrt[]{16x^4} \\ a=4x^2 \\ \\ b^2=36 \\ \sqrt[]{b^2}=\sqrt[]{36} \\ b=6 \end{gathered}[/tex]Substituting a and b we get that
[tex]\begin{gathered} 16x^4-36=(4x^2+6)(4x^2-6) \\ \\ \text{We can further factor this to} \\ (4x^2+6)(4x^2-6)=2\cdot(2x^2+3)\cdot2(2x^2-3) \\ \\ \text{Simplifying it we have} \\ 4(2x^2+3)(2x^2-3) \\ \text{as our factor} \end{gathered}[/tex]Which expression is equivalent to 2n + 4 (3n – 1) + 5?
Answers
Weare asked to reduce the expression
2 n + 4 (3 n -1) + 5 in order to compare it with other expressions given.
so we proceed to apply distributive property to eliminate the parenthesis:
2 n + 12 n - 4 + 5
now we combine like terms:
14 n + 1
Please check for this expression among the answers you were provided.
how do I find the area of this shape ?
Answers
So this is a shape that can be subdivide into triangles and squares.
So let us first consider the triangle with dimensions 2 and 6. As it is clear that it forms a right angled triangle, the area is,
[tex]\frac{1}{2}6\times2=6[/tex]Then there is a square of each side 2. So the area is, 4; since(2*2).
Then there is another triangle of dimneions 2 each . Thus the area is,
[tex]\frac{1}{2}2\times2=2[/tex]And again there forms a traingle with base 4 and height 10; (2+2+6 from the dotted lines.). Its area is,
[tex]\frac{1}{2}\times4\times10=20[/tex]So the total area is, 6+4+2+20=32.
The quotient of thrice a number and the number Translate into a variable
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Ok, so
Here we have the expression:
The quotient of thrice a number and the number.
First, let "x" be the number.
If "x" is the number, the sentence "thrice the number" can be written as 3x.
Now, the quotient of thrice a number (3x) and the number (x), will be:
[tex]\frac{3x}{x}[/tex]If we simplify, this is 3.
The area of a rectangle is 48cm². The length is three times the width.what is the length of the rectangle?
Answers
The length of the rectangle = 12 cm
Explanations:Let the area be represented by A
Let the length be represented by L
Let the width be represented by W
The area of the rectangle = 48cm²
A = 48cm²
The length is three times the width
L = 3W
Area = Length x Width
A = LW
48 = 3W(W)
48 = 3W²
W² = 48/3
W² = 16
W = √16
W = 4 cm
L = 3W
L = 3(4)
L = 12 cm
The length of the rectangle = 12 cm
the last tutor gave me the wrong answer can you pleas pleas help
Answers
Given that:
- The store pays $54 for the jar of fossils.
- It marks up the price by 5%.
Let be "x" the new price (in dollars).
In order to write the percent as a Decimal Number, you need to divide it by 100. Then:
[tex]\frac{5}{100}=0.05[/tex]Therefore, 5% of $54 is:
[tex](\text{ \$}$54$)(0.05)=\text{ \$}$2.7$0[/tex]Then, the new price is:
[tex]\begin{gathered} x=\text{ \$}$54$+\text{ \$}2.70 \\ x=\text{\$}$56.7$0 \end{gathered}[/tex]Hence, the answer is:
[tex]\text{\$}$56.7$0[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 4". Find P(A). Outcome Probability 1 0.06 2 0.41 3 0.03 4 0.37 5 0.13
Answers
A is ,divisor of 4
P(A) = ?
For every number , 1 in 4 are divisors of 4
4 = 4•1 = 2•2
then probability is sum of
P(A) = P(4) = 0.37
P(2) = 0.41
P(1) = 0.06
P(A) = 0.37 + 0.41 + 0.06 = 0.84
Then answer is
P(A) = 0.84
Practice1. Solve each equation.a. O = x2 – 7x – 18c. O = x2 - 10x + 12e. 3x2 – 22x + 7 = 02. Determine the roots of each equation. CIa. y = y2 + 9x + 3
Answers
Okay, here we have this:
We need to solve the following equation:
[tex]0=x^2-10x+12[/tex]We are going to solve using the general formula for equations of the second degree:
[tex]\begin{gathered} x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4\cdot1\cdot12}}{2\cdot1} \\ =\frac{10\pm\sqrt[]{100-48}}{2} \\ =\frac{10\pm\sqrt[]{52}}{2} \\ =\frac{10\pm2\sqrt[]{13}}{2} \\ =5\pm\sqrt[]{13} \end{gathered}[/tex]Finally we obtain that the answers are:
x₁=5+√13
x₂=5-√13
When both sides of an any quality or multiplied or divided by a negative number the inequality symbol switches from less than 2 greater than or greater than to less than in the inequality is said to be preserved or reserved.
Answers
Recall that an inequality symbol is preserved under any addition or subtraction, but it REVERSES (flips) direction when you multiply both sides OR divide both sides by a negative number.
So the greater tahn symbol changes to a less than symbol and vice versa:
a < b whne you multiply (or divide) by for example (-2) negative two becomes:
-2 a > -2 b
It switches form < to > or vice versa (from > to <)
Patients wait 126 days on average for a heart transplant with a standard deviation of 24 days. Whatproportion waits fewer than 90 days? (enter theanswer as a percent rounded to the nearesthundredth as needed)
Answers
Answer:
6.68%
Explanation:
• Average Wait Period = 126 days
,• Standard Deviation = 24 days
,• X=90 days
First, we find the z-score using the z-score formula:
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ z=\frac{90-126}{24}=-\frac{36}{24}=-1.5 \end{gathered}[/tex]Next, we find the proportion that waits fewer than 90 days, i.e. P(z<-1.5).
From the z-score table:
[tex]\begin{gathered} P(z<-1.5)=0.066807 \\ =6.68\% \end{gathered}[/tex]The proportion that waits fewer than 90 days is 6.68%.
A very large bag contains more coins than you are willing to count. Instead, you draw a random sample of coins from the bag and record the following numbers of eachtype of coin in the sample before returning the sampled coins to the bag. If you randomly draw a single coin out of the bag, what is the probability that you will obtaineither a nickel or a penny? Enter a fraction or round your answer to 4 decimal places, if necessary.Quarters24Coins in a BagDimes Nickels2822Pennies26
Answers
First, find the probability for drawing a nickel and drawing a penny.
[tex]\begin{gathered} P(N)=\frac{\text{number of sampled nickel}}{\text{total number of sampled coins}} \\ P(N)=\frac{22}{24+28+22+26} \\ P(N)=\frac{22}{100} \\ \\ P(Pn)=\frac{\text{number of sampled penny}}{\text{total number of sampled co}\imaginaryI\text{ns}} \\ P(Pn)=\frac{26}{22+28+22+26} \\ P(Pn)=\frac{26}{100} \end{gathered}[/tex]Since finding a nickel and finding a penny are mutually exclusive events, then we can say that
[tex]\begin{gathered} P(N\text{ or }Pn)=P(N\cup Pn) \\ P(N\cup Pn)=P(N)+P(Pn) \\ P(N\cup Pn)=\frac{22}{100}+\frac{26}{100} \\ P(N\cup Pn)=\frac{48}{100} \\ P(N\cup Pn)=0.48 \end{gathered}[/tex]Therefore, the probability of finding a nickel or a penny is 0.48.
Let f(x) = x + 3 and g(x) =The graph of (fºg)(x) is shown below.X:
Answers
We want the range of (f o g)(x).
The range is the set of y-values for which a function is defined.
Looking at the graph, we can see that the rational function graph as a horizontal asymptote at y = 3. Otherwise, the function is defined for all real values of y.
Thus, we can say that the range is all real values of y EXCEPT y = 3.
From the answer choices,
third choice is right
"all real numbers except y = 3"