Using the normal distribution, it is found that:
81.85% of bags has between 1026 and 1380 chocolate chips.15.87% of the bags contain fewer than 1144 chocolate chips.2.28% of bags contain more than 1498 chocolate chips.Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the number of chips are given as follows:
[tex]\mu = 1262, \sigma = 118[/tex]
The proportion of bags that has between 1026 and 1380 chocolate chips is the p-value of Z when X = 1380 subtracted by the p-value of Z when X = 1026, hence:
X = 1380:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1380 - 1262)/118
Z = 1
Z = 1 has a p-value of 0.8413.
X = 1026:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1026 - 1262)/118
Z = -2
Z = -2 has a p-value of 0.0228.
0.8413 - 0.0228 = 0.8185.
Hence the percentage is 81.85%.
The proportion that has fewer than 1144 chips is the p-value of Z when X = 1144, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1144 - 1262)/118
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the percentage is of 15.87%.
The proportion that has more than 1498 chips is one subtracted by the p-value of Z when X = 1498, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1498 - 1262)/118
Z = 2
Z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
Hence the percentage is of 2.28%.
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6. Keaton needs to fill juice cups for her little sister's birthday party. There are 22 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
(1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
Answer: she will need about 2 gallons of juice
Step-by-step explanation:
A group of students is playing a game of El Repollo, which involves passing a ball made of layers of paper. After catching the ball, a player peels off a layer of paper, answers a question that has been written on the paper, and then tosses the ball to the next player. . Sara tosses the ball to Alex from a height of 1.5 meters. • The ball reaches its highest point about 1 second later. • Alex misses the ball, and it hits the ground 2 seconds after Sara tosses it to him. Which function approximates the height of the ball, in meters, a seconds after Sara tosses it to Alex? f(x) = -5z²+9.25z + 1.5 f(x) = 5(x-1.5)(x-2) f(x) = -5x(x - 2) f(z) = 5x² -10.75z + 1.5
The quadratic function that approximates the height of the ball, in meters, seconds after Sara tosses it to Alex is:
y = ax² + bx + 1.5.
What is a quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
Considering the context of this problem, we will use equations to find the coefficients.
Sara tosses the ball to Alex from a height of 1.5 meters, meaning that the initial height is of 1.5 meters, thus the coefficient c has a value of 1.5, and:
y = ax² + bx + 1.5.
The ball reaches its highest point about 1 second later, hence the x-coordinate of the vertex is calculated as follows:
xv = -b/2a = 1
-b = 2a
b = -2a
The ball hits the ground 2 seconds after Sara tosses it to him, hence y(2) = 0, that is:
0 = 4a + 2b + 1.5
4a + 2b = -1.5.
2a + b = -1.5.
2a - 2a = -1.5.
(undefined function, there is a small typo in the problem but the procedure is shown in this problem, we just have to solve the system of equations for a and b).
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a..
H=119 ft
A. Write the ratio of height of the building to the number of floors. Then, find the unit rate, and explain what it means in this situation. Fill in the correct answers to complete the sentences.
The ratio of height of the building to the number of floors is 119/7 and the unit ratio is 17 which means that the height of each floor is 17 ft.
In the given question,
The height of a building is proportional to the number of floors.
In the building have 7 floors.
That means, n = 7
the height of building H = 119 ft.
Since the height of a building is proportional to the number of floors.
So [tex]\frac{H}{n}=k[/tex] where k = constant.
Firstly we have to find the ratio of height of the building to the number of floors.
As we know, H = 119 ft, n = 7
So the ratio,
[tex]\frac{H}{n}=\frac{119}{7}[/tex]
The ratio of height of the building to the number of floors is 119/7.
Now we have to find the unit rate.
To find the unit rate we have to divide the height of building to the number of floors.
As we know,
[tex]\frac{H}{n}=\frac{119}{7}[/tex]
now simplifying the ratio by dividing the both number by 7
Unit ratio [tex]=\frac{H}{n}[/tex]
Unit ratio [tex]=\frac{119/7}{7/7}[/tex]
Unit ratio [tex]=\frac{17}{1}[/tex]
Unit ratio = 17
Hence, the unit ratio is 17 ft which means that the height of each floor is 17 ft.
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Titus drew circle with his Compass the circle has five central angles for the angles measure 55° 37 degrees 96 degrees and 88 degrees what is the degree measure of a central angle.
The measure of the unknown central angle is 84°.
We are given that Titus drew a circle with the compass. The circle has five central angles, which measure 55°, 37°, 96°, 88°, and one of the angles is unknown.
A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.
We know that the measure of the complete angle is 360°. Thus, the sum of all the central angles must be equal to 360°. Let the measure of the unknown angle be "x". The equation is given below :
55° + 37° + 96° + 88° + x = 360°
276° + x = 360°
x = 84°
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The captain of a ship at sea sights a lighthouse which is 100 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 26°. How far is the ship from the base of the lighthouse? How many feet?
Answer:
Explanation;
The set will be a right angled triangle as shown;
Which statement BEST describes the effect on the value of y when the value of x isdoubled?
This is a linear function whose graph cuts the origin.
Therefore, any increase in the x axis will lead to a corresponding increase in the y axis by the same factor.
[tex]\begin{gathered} \text{The graph has the equation y =}\frac{x}{2} \\ If\text{ x is doubled, the corresponding value of y is also doubled} \end{gathered}[/tex]Thus, C is the answer
7. The graph was made to compare the costs of renting copy machinesfrom Ames Business Product to those from Beck's Office Supply. Whatinformation is given by the point of intersection of the two lines? *
Notice that the y-axis of the given graph represents the total cost per month, and the x-axis represents the number of copies made in that month, therefore, the x-entry of the intersection of the graphs represents the number of copies for which the total cost per month is the same for both companies.
Answer: Last option.
Take a guess: A student takes a multiple-choice test that has 9 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places. (a) Find P(3). (b) Find P (More than 1).
The probability that the student guesses 3 question correctly is 0.234 and the probability that the student guess more than one correctly is 0.7.
Using the property of binomial distribution we can calculate that the probability that a answer is correct is 0.25
As there are 4 options , hence we will see that probability that an option picked is correct is 1/4 = 0.25
Now we have to find the probability for 3 answers to be correct .
We will use the formula
[tex]P(X=x) = \frac{n!} {x! (n - x)!} \cdot p^x \cdot (1 - p)^{n - x}[/tex]
Now putting the values of x = 3 and the value of p = 0.25 we get
P(X = 3) = 0.234
therefore the value of P(3) = 0.234
Now we have to find the value of P(x>1)
Using the same formula we calculate the occurrence of the event
P(x>1)=1-P(x≤1)
or, P(x>1) = 0.7
Hence the required probability is 0.7.
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Identify the number as prime Kompass it or neither if the number is comp is it rated as the product of prime factors 133
Given the number 133, we list the first prime numbers and then look for a possible factor of 133:
Prime_list = {2, 3, 5, 7, 11, ...}
133 is not an even number, so we discard 2. 133 does not end with 0 or 5, so 5 can not be a factor. We evaluate 3, 7, and 11:
The only division with no rest is 133/7 = 19, and we know that 7 and 19 are prime numbers. We conclude that 133 is composite and can be represented as a product of 7 and 19:
[tex]133=7\cdot19[/tex]I’m in major need of help for this question I honestly do not understand it
Answer
Explanation
Given the figure, we can deduce the following information:
a and b cut by transversal lines
To determine the value of x, we redraw the figure as shown below:
Since a and b are parallel lines, y must be equal to 36°. We also note that the angles on a straight add up to 180°. So,
[tex]\begin{gathered} 36+65+x=180 \\ \text{Simplify and rearrange} \\ x=180-65-36 \end{gathered}[/tex]Therefore, the equation that can be used to solve for x is:
[tex]x=180-65-36[/tex]Now, we get the value of x:
[tex]\begin{gathered} x=180-65-36 \\ \text{Calculate} \\ x=79\degree \end{gathered}[/tex]Therefore, the value of x is 79°.
(Combining Equations)What is the result of adding these two equations ? 5x - y = 6 -2x + y = 8
Answer:
3x=14
Explanation:
Given the two equations:
[tex]\begin{gathered} 5x-y=6 \\ -2x+y=8 \end{gathered}[/tex]Adding the two equations gives:
[tex]\begin{gathered} \lbrack5x+(-2x)\rbrack+\lbrack-y+y\rbrack=6+8 \\ \lbrack5x-2x\rbrack+0=14 \\ 3x=14 \end{gathered}[/tex]XB is the angle bisector of ZAXC. MZAXB23А.BVхC с
To obtain x, we can sum the angles < AQB and < BQC
=> 5X + 8X - 24
=> 13X -24
we are also told that that the sum of their angles is 80
13X - 24 = 80
13 X = 24 + 80
13X = 104
Divide both sides by 13
x = 104/13
x = 8
A fair die is rolled two times. What is the probability that both rolls are 3?
A) 0.028
B) 0.083
C) 0.167
D) 0.0046
Answer:
b)
Step-by-step explanation:
this is so becuz a fair die contains or has six parts meaning if its rolled once there are 6 probabilities so if its rolled twice the probabilities increase the chances are (1,1),(1,2),(1,3)... to (1,6) there is only one probability that its(3,3) so giving u 1/12 which when divided hives u b)
Find the y intercept of the line on the graph.
Answer: the y-intercept is -3
Step-by-step explanation:
if you ever need to find the y-intercept, here is how to do it:
the y-axis is the line that goes up and down. wherever the line from the equation crosses that y-axis line, that is going to be the y-intercept. as you can see here, they intercept at -3.
if k is the midpoint of CT , CK =3x+23,and KT =5x+7,then find x and CT
Given:
CK = 3x + 23
KT = 5x + 7
If K is the midpoint of CT, then CK = KT. Then,
[tex]3x+23=5x+7[/tex]Finding x:
Subtracting 3x from both sides:
[tex]\begin{gathered} 3x+23-3x=5x+7-3x \\ 23=2x+7 \end{gathered}[/tex]Subtracting 7 from both sides:
[tex]\begin{gathered} 23-7=2x+7-7 \\ 16=2x \end{gathered}[/tex]And dividing both sides by 2:
[tex]\begin{gathered} \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}[/tex]x = 8.
Finding CT:
K is the midpoint of CT, then CT = CK + KT
[tex]\begin{gathered} CT=3x+23+5x+7 \\ CT=3*8+23+5*8+7 \\ CT=24+23+40+7 \\ CT=94 \end{gathered}[/tex]CT = 94.
Answer:
x = 8
CT = 94
Given P(A)=0.31P(A)=0.31, P(B)=0.5P(B)=0.5 and P(A\text{ or }B)=0.585P(A or B)=0.585, find the value of P(A\text{ and }B)P(A and B), rounding to the nearest thousandth, if necessary.
Given:
P(A) = 0.31
P(B) = 0.5
P(A or B) = 0.585
To find:
P(A and B)
To determine P(A and B), we will apply the formula:
[tex]P(A\text{ or B\rparen}=\text{ P\lparen A\rparen + P\lparen B\rparen}-\text{ P\lparen A and B\rparen}[/tex][tex]\begin{gathered} substitute\text{ the values:} \\ 0.585\text{ = 0.31 + 0.5 +- P\lparen A and B\rparen} \\ 0.585\text{ = 0.81 - }P(A\text{ and B\rparen} \\ 0.585+\text{ P\lparen A and B\rparen = 0.81} \\ P(A\text{ and B\rparen = 0.81 - 0.585} \end{gathered}[/tex][tex]P(A\text{ and B\rparen = 0.225 }[/tex]Find the scale factor of the line segment dilation. AB: endpoints (-6, -3) and (-3,-9) to A'B': endpoints at (-2, -1) and (-1, -3). A) -1/3 B) 1/3 C) 3D) -3
we know that the endpoints of AB are
[tex]\begin{gathered} (x_1,y_1)=\mleft(-6,-3\mright) \\ (x_2,y_2)=(-3,-9) \end{gathered}[/tex]and the distance formula is given by
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]By substituying these points, we have that
[tex]d=\sqrt[]{(-3-(-6))^2+(-9-(-3))^2}[/tex]which is equal to
[tex]\begin{gathered} d=\sqrt[]{(-3+6)^2+(-9+3)^2} \\ d=\sqrt[]{3^2+(-6)^2} \end{gathered}[/tex]then
[tex]\begin{gathered} d=\sqrt[]{9+36} \\ d=\sqrt[]{45} \\ d=\sqrt[]{9\cdot5} \\ d=\sqrt[]{9}\cdot\sqrt[]{5} \\ d=3\sqrt[]{5}\ldots..(A) \end{gathered}[/tex]On the other hand, if
[tex]\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-1,-3) \end{gathered}[/tex]similarly to the previous case, the distance between the endpoint for A'B' is
[tex]d=\sqrt[]{(-1-(-2))^2+(-3-(-1))^2}[/tex]which is equal to
[tex]\begin{gathered} d=\sqrt[]{(-1+2)^2+(-3+1)^2} \\ d=\sqrt[]{1^2+(-2)^2} \\ d=\sqrt[]{1+4} \\ d=\sqrt[]{5}\ldots..(B) \end{gathered}[/tex]Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.
Then, the answer is B.
I need help!!!! Please I'm not good at this:(
The values of the numbers will be:
1. 162
2. 162
3. 1 99/100.
4. 11.4
5. 72
How to calculate the values?1. 6³ - 8² + 300 ÷ ( 5 + 5)²
It should be noted that this will follow the rules or PEDMAS. This implies that the parentheses will be solved first and that subtraction comes last.
6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
2. 6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
3. (1/5 + 1/2)² + 3/10 × 5
= (7/10)² + 3/10 × 5
= 49/100 + 1 1/2
= 1 99/100
4. 8.1 ÷ 0.9 + 0.4³ ÷ 0.8 × 30
= 9 + 0.064 ÷ 0.8 × 30
= 9 + 0.08 × 30
= 9 + 2.4
= 11.4
5. (18 - 4² + 2)² / (1 ÷ 4 1/2)
= 4² / 2/9
= 16 × 9/2
= 72
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1. On a bookshelf containing 17 novels, 5 of them were written by Stephen King. If Sheri selects one at random, find the probability that she does not choose a Stephen King novel. Give your answer as a reduced fraction.
2. In a company there are 11 executives: six women and five men. Four are selected to attend a management seminar. Find the probability that one woman and three men are selected. Give your answer as a reduced fraction.
The probability that she does not choose a Stephen king novel is 12/17.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Given,
1) total books no shelf = 17
Novel of Stephen king = 5
The probability of stephen king = 5/17
The probability of not choosing Stephen novel = 1-5/17
= (17-5)/17
=12/17
2) total number of executives = 11
Number of men = 5
Number of women = 6
probability of a man = 5/11
Probability of a woman = 6/11
Given, one woman and 3 men are selected
therefore, using combination.
Total combinations = n! / (r! x (n - r)!)
n = 4
r = 3
Therefore, probability = n! / (r! x (n - r)!)[tex](5/11)^{1} (6/11)^{3}[/tex]
=4!/3!(1!)(5/11)^{1} (6/11)^{3}
=4(5/11)(216/1331)
=4320/14641
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For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?
m greater-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 49 Over 12 EndFraction
Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
As given in the question,
Given graph equation:
y = 3x² + 7x + m
Graph y = 3x² + 7x + m has two x-intercepts if and only if
3x² + 7x + m<0 __(1)
Formula used to calculate x value is x = -b/2a
Compare with the standard form:
a= 3
b=7
c=m
x= -7/ 2(3)
= -7/6
Substitute x=-7/6 in (1)
3(-7/6)² + 7(-7/6) +m<0
⇒49/12 -49/6 +m <0
⇒-49/12 +m<0
⇒m< 49/12
Therefore, Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
The complete question is:
For what values of m does the graph of y = 3x²+ 7x + m have two x-intercepts?
a. m > 25/3
b. m < 25/ 3
c. m < 49 /12
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what is the circumference of a circle with a radius of 6cm
The circumferance of a circle with radius of 6cm is 37.68cm
To find:
Circumferance of a circle
Given:
Radius of circle is 6cm
Solution:
Circumference is similar to perimeter as it is the total length required to draw a circle.
Let c be the perimeter.
c = 2πr
or
c = πd
This depends on knowing the radius (r) or diameter (d).
For example, let's calculate it manually.
If r = 6 cm, the circumference in π is c = 2π(6) = 12π cm.
When expressed numerically, it is 37.7 cm after the decimal point is rounded off.
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What is the distance between the following points?The answer choices areA- 9B- 10C- square root of 21D- square root of 58
Given:
Points: (3, -9) and (6, -2) on a coordinate plane
To find:
The distance between the two points
To determine the distance between the points, we will apply the formula:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} x_1=3,y_1=-9,x_2=6,y_2\text{ = -2} \\ dis\tan ce\text{ = }\sqrt{(-2-(-9))^2+(6-3)^2} \\ dis\tan ce\text{ = }\sqrt{(-2+9)^2+(6-3)^2} \\ dis\tan ce\text{ = }\sqrt{(7)^2+(3)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ = }\sqrt{49\text{ + 9}} \\ distance\text{ = }\sqrt{58} \end{gathered}[/tex]Skill plansTX StandaScienceRecommendationsA Math49 Language artsSocial studiesAlgebra 1> 0.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! GotWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Kaylee is selling her handmade jewelry online. Yesterday, she sold 9 bracelets and 3necklaces, for a profit of $144. Today, she made a profit of $279 by selling 10 bracelets and 9necklaces. How much profit does Kaylee earn from each piece?Kaylee earns a profit of $|| from every bracelet and $from every necklace.Submit
Let x be the profit of a bracelet and y the profit of a necklace.
Yesterday she sold: 9 bracelets and 3 necklaces, for a profit of $144:
[tex]9x+3y=144[/tex]Today, she made a profit of $279 by selling 10 bracelets and 9 necklaces:
[tex]10x+9y=279[/tex]System of equations:
[tex]\begin{gathered} 9x+3y=144 \\ 10x+9y=279 \end{gathered}[/tex]To solve by elimination:
1. Multiply the first equation by -3:
[tex]\begin{gathered} -3(9x+3y=144 \\ \\ -27x-9y=-432 \end{gathered}[/tex]2. Add equation you get in step 1 and the second equation in the system:
[tex]-17x=-153[/tex]3. Use the equation you get in step 2 to solve x:
[tex]\begin{gathered} \text{Divide both sides of the equation into -17} \\ \\ \frac{-17}{-17}x=\frac{-153}{-17} \\ \\ x=9 \end{gathered}[/tex]4. Use the value of x to solve y:
[tex]\begin{gathered} 9x+3y=144 \\ \\ 9(9)+3y=144 \\ 81+3y=144 \\ \\ \text{Subtract 81 in both sides of the equation:} \\ 81-81+3y=144-81 \\ 3y=63 \\ \\ \text{Divide both sides of the equation into 3:} \\ \frac{3}{3}y=\frac{63}{3} \\ \\ y=21 \end{gathered}[/tex]Then, the solution for the system is :
[tex]\begin{gathered} x=9 \\ y=21 \end{gathered}[/tex]Kaylee earns a profit of $9 from every bracelet and $21 from every necklace
not all tiles would be used, need help solving the steps for a bisecting line statement.
We have different steps for bisecting a line segment using a reflective device, and these steps are as follows:
And we have to select three of them to complete the process.
To determine the steps, we need to remember that the reflective device permits us to see through it, and also see reflections on it. Then the steps for bisecting a line segment AB are:
1. Place the reflective device anywhere on the segment - It does not matter the position at which we need to put the reflective device.
2. Move the reflective device around on the paper until the reflection of point A coincides with point B.
3. Draw the line of the reflection using the edge of the reflective device as a guide.
Therefore, in summary, the three steps are:
• Place the reflective device anywhere on the segment (,first box,).
,• Move the reflective device around on the paper until the reflection of point A coincides with point B (,third box,).
• Draw the line of the reflection using the edge of the reflective device as a guide (sixth box),.
which value of y makes the inequality 3y^2+2(y-5)>8 true?
A. y = 0
B. y = –1
C. y = –2
D. y = –3
The function y=3.75+2.50(x-3) can be used to determine the cost of dollars for a uber ride of x of miles. What is the rate of change of the cost in dollars with respect to the number of miles?
function y = 3.75 + 2.5(x - 3)
dy/dx = 0 + 2.5 - 0
dy/dx = 2.5
The rate of change of the cost in dollars = 2.5
Find the y-intercept of the line on the graph.
The y-intercept of the line on the graph is -2.
What is termed as the y-intercept?The point at which the graph intersects a y-axis is known as the y-intercept. Finding the intercepts of any function of the form y = f(x) is critical when graphing. A function can have one of two types of intercepts. They are known as the x and y intercepts. An intercept of a function is the point at which the function's graph intersects the axis. A graph's y intercept is the point at which the graph intersects the y-axis. We know that any point just on y-axis has an x-coordinate of 0. As a result, the x-coordinate of the a y-intercept is 0.For the given question;
The graph of the straight line is given.
The y-intercept of the line is the point on y axis where the value of the x becomes zero.
At x = 0, y = -2.
Thus, he y-intercept of the line on the graph is -2.
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3. Given: BAM is a right angle. If m BAM=4x+22, then solve for the value of x.
Right angle means that the angle is equal to 90 degrees
We will thus proceed by equating BAM = 90 degrees, we have:
[tex]\begin{gathered} 4x+22=90 \\ \text{Subtract 22 from both sides, we have:} \\ 4x+22-22=90-22 \\ 4x=68 \\ \text{divide through both sides by 4, we have:} \\ \frac{4x}{4}=\frac{68}{4} \\ x=17^{\circ} \end{gathered}[/tex]x = 17
Answer: 17 degrees
Step-by-step explanation:
<BAM is a right angle. A right angle is defined to be 90 degrees.
So...
<BAM = 4x + 22 is transformed to 90 = 4x + 22
90 = 4x + 22
4x = 90 - 22
4x = 68
x = 17 degrees
Solve each equation Show steps for credit4. 5+y=75.8=2+q6.6=n-4
Answer:
• y=2
,• q=6
Explanation:
Number 4
Given the equation:
[tex]5+y=7[/tex]To solve for y, subtract 5 from both sides:
[tex]\begin{gathered} 5+y-5=7-5 \\ y=2 \end{gathered}[/tex]The value of y is 2.
Number 5
Given the equation:
[tex]8=2+q[/tex]To solve for q, subtract 2 from both sides:
[tex]\begin{gathered} 8-2=2-2+q \\ q=6 \end{gathered}[/tex]The value of q is 6.
A Christmas tree is supported by a wire that is 9 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 23 meters shorter than the height of the tree. What is the height of the tree?
Through the given statement measurements we find that the height of the tree is = 33 m.
What is Pythagoras Theorem?The right-angled triangle's relationship between its sides is explained by the Pythagorean Theorem, often known as Pythagoras Theorem, a key concept in mathematics.
The Pythagorean triple describes the sides of the right triangle. For the most part, the Pythagorean theorem is employed to determine a triangle's angle and the length of an ambiguous side.
The base, perpendicular, and hypotenuse formulas are derived by means of this theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides.
As it is on the other side of the angle of 90 degrees, the hypotenuse in this case is the longest side.
An equation, commonly known as a Pythagorean triple, is created by squared values for the sides of a right triangle that have positive integer values.
Let the Height of the Christmas tree be 'h' meters.
Length of the wire = (h + 9) meters
Distance from the base = (h - 23) meters
This scenario forms a right-angled triangle, with height = h m, base = (h-23) m and hypotenuse = (h+9) m
Now, as this is a right-angled triangle,
h^2 + (h-23) ^2 = (h+9) ^2 (Pythagoras theorem)
⇒ h^2 + h^2 - 46h + 529 = h^2 + 18h + 81
⇒ 2h^2 - h^2 - 46h - 18h = 81 - 529
⇒h^2 - 64h = -448
⇒ h^2 - 64h + 448 = 0
⇒ h^2 - (56 + 8) h + (56 x 8) = 0
⇒ (h - 56) x (h - 8) = 0
⇒ h = 56 or h = 8
Since the distance from the base = (h - 23) m cannot be a negative value,
therefore, h = 56 m
Therefore,
The height of the tree = 56 m,
The length of the wire = h + 9 = 56 + 9 = 65 m
The distance from the base of the tree to the wire = h -23
= 56 - 23 = 33 m
To learn more about Pythagoras Theorem, refer to:
brainly.com/question/21926466
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