100 POINTS!!!!!!!!!!!!!!1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION
Answers
In triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).
In the next given equilateral triangle ABC, y = 70°.
Finding m∠BHA:
In triangle ABC, it is given that,
∠B = 90°
And m∠A : m∠C = 1:2
Let us assume m∠A is x. Then, m∠C = 2x
According to the angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
90° + x + 2x = 180°
90° + 3x = 180°
3x = 90°
x = 30°
⇒ In triangle ABC, ∠A = 30° and ∠C = 60°
Now, in triangle AHB, it is also given that,
BH = AH
⇒ ∠ABH = ∠A = 30°
Thus, according to the angle sum property of a triangle,
∠ABH + ∠A + ∠BHA = 180°
30° + 30° + ∠BHA = 180°
∠BHA = 180° - 60°
∠BHA = 120°
Finding y in the Second Triangle:
Since triangle ABC is equilateral,
∠A = ∠B = ∠C = 60°
∴ x + 2x + 3x = 60°
6x = 60°
x = 10°
In triangle ABD, using angle sum property of triangle,
x + ∠B + ∠BDA = 180°
10° + 60° + ∠BDA = 180°
∠BDA = 180° - 70°
∠BDA = 110°
Now, since, ∠BDA and y are linearly adjacent angles,
∠BDA + y = 180°
110° + y = 180°
y = 180° - 110°
y = 70°
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Related Questions
Graph the line with a slope of −1 that contains the point (3,6).
Answers
Answer:
The equation of the line is y = -1.x + 9
Graph is provided in the attached figure
Step-by-step explanation:
The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation
[tex]y = mx + c[/tex]
where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0
Given slope = -1, we can find c and the equation of the line
Since (3,6) is a point on the graph, these coordinates must satisfy the above equation
Substitute for y = 6 and x = 3
[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]
In the attached figure you can see that (3,6) is on the line
i. 749x98+749 x2 ii. 62 x 999 +4795 iii. 736 x 97 iv. 258 x 1008
solve these using distributive property
pls help if u know
Answers
Step-by-step explanation:
I= 74810
II=66733
III=71392
iv=239904
how do i write 4x+5y=20 in slope intercept form
Answers
Answer:
Y=mx+b
Step-by-step explanation:
The answer is y = -4/5x + 4.
We know the general form for slope intercept form is :
y = mx + c
The given equation is in standard form.
4x + 5y = 20
Bring 4x to the other side by subtracting 4x on both sides.
4x + 5y - 4x = 20 - 4x
5y = -4x + 20
Divide 5 on both sides to isolate the variable y.
5y x 1/5 = 1/5 x (-4x + 20)
y = -4/5x + 4
Factor.
3x² +7x
I don’t know what to do
Answers
Answer:
Most you can do is factor out the x and turn it into x (3x + 7)
roots would be x = 0 and x = -7/3
Answer: x(3x+7)
Step-by-step explanation:
You would factor the x out of both of your values and put on the outside of the parenthesis. And you put the two numbers that you have left inside of the parenthesis. And that is as far down as this function can be factored.
Consider the spiral curves given parametrically by: (see picture and answer question)
Answers
a. The arc length is given by the integral
[tex]L(r) = \displaystyle \int_3^\infty \sqrt{x'(t)^2 + y'(t)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\left(\frac{t\cos(t) - r\sin(t)}{t^{r+1}}\right)^2 + \left(-\frac{t\sin(t) + r\cos(t)}{t^{r+1}}\right)^2} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \sqrt{\frac{(t^2+r^2)\cos^2(t) + (t^2+r^2)\sin^2(t)}{\left(t^{r+1}\right)^2}} \, dt \\\\ ~~~~~~~~ = \boxed{\int_3^\infty \frac{\sqrt{t^2+r^2}}{t^{r+1}} \, dt}[/tex]
b. The integrand roughly behaves like
[tex]\dfrac t{t^{r+1}} = \dfrac1{t^r}[/tex]
so the arc length integral will converge for [tex]\boxed{r>1}[/tex].
c. When [tex]r=3[/tex], the integral becomes
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2+9}}{t^4} \, dt[/tex]
Pull out a factor of [tex]t^2[/tex] from under the square root, bearing in mind that [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex].
[tex]L(3) = \displaystyle \int_3^\infty \frac{\sqrt{t^2} \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{|t| \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{t \sqrt{1+\frac9{t^2}}}{t^4} \, dt \\\\ ~~~~~~~~ = \int_3^\infty \frac{\sqrt{1+\frac9{t^2}}}{t^3} \, dt[/tex]
since for [tex]3\le t<\infty[/tex], we have [tex]|t|=t[/tex].
Now substitute
[tex]s=1+\dfrac9{t^2} \text{ and } ds = -\dfrac{18}{t^3} \, dt[/tex]
Then the integral evaluates to
[tex]L(3) = \displaystyle -\frac1{18} \int_2^1 \sqrt{s} \, ds \\\\ ~~~~~~~~ = \frac1{18} \int_1^2 s^{1/2} \, ds \\\\ ~~~~~~~~ = \frac1{27} s^{3/2} \bigg|_1^2 \\\\ ~~~~~~~~ = \frac{2^{3/2} - 1^{3/2}}{27} = \boxed{\frac{2\sqrt2-1}{27}}[/tex]
a) The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) r > 1 for a spiral with finite length.
c) The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
How to characterize and analyze a group of parametric functions
a) The arc length formula for 2-dimension parametric functions is defined below:
L = ∫ √[(dx / dt)² + (dy / dt)²] dt, for [α, β] (1)
If we know that [tex]\dot x (t) = \frac{t \cdot \cos t - r \cdot \sin t}{t^{r+1}}[/tex], [tex]\dot y(t) = \frac{t\cdot \sin t + r\cdot \cos t}{t^{r + 1}}[/tex], α = 0 and β → + ∞ then their arc length formula is:
[tex]L = \int\limits^{\infty}_{3} {\sqrt{\left(\frac{t\cdot \cos t - r\cdot \sin t}{t^{r + 1}}\right)^{2}+\left(\frac{t\cdot \sin t + r\cdot \cos t}{t^{r+1}}\right)^{2}} } \, dt[/tex]
By algebraic handling and trigonometric formulae (cos ² t + sin² t = 1):
[tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex] (2)
The improper integral in simplified form is equal to [tex]L = \int\limits^{\infty}_{3} {\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}} } \, dt[/tex].
b) By ratio comparison criterion, we notice that √(t² + r²) is similar to √t² = t and [tex]\frac{\sqrt{t^{2}+r^{2}}}{t^{r + 1}}[/tex] is similar to [tex]\frac{t}{t^{r +1}} = \frac{1}{t^{r}}[/tex].
The integral found in part a) has a finite length if and only the governing grade of the denominator is greater that the governing grade of the numerator. and according to the ratio comparson criterion, the absolute value of the ratio is greater than 0 and less than 1. Therefore, r > 1 for a spiral with finite length.
c) Now we proceed to integrate the function:
L = ∫ [√(t² + 9) / t⁴] dt, for [3, + ∞].
L = ∫ [t · √(1 + 9 / t²) / t⁴] dt, for [3, + ∞].
By using the algebraic substitutions: u = 1 + 9 / t², du = - (18 / t³) dt → - (1 / 18) du.
L = ∫ √u du, for [3, + ∞].
L = - (1 / 9) · √(u³), for [3, + ∞].
L = - (1 / 9) · [√(1 + 9 / t²)³], for [3, + ∞].
L = - (1 / 9) · [√(2³) - √(1³)]
L = - (1 / 9) · (2√2 - 1)
L = (1 - 2√2) / 9
The length of the spiral when r = 3 is (1 - 2√2) / 9 units.
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In a mathematics class, half of the students scored 87 on an achievement test.
With the exception of a few students who scored 52, the remaining students
scored 71. Which of the following
statements is true about the distribution of
scores?
Answers
Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Therefore, the correct answer is option A. The mean is less than the median.
What are statistics?Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Half the students scored 87.
The next highest score exists at 71.
Then the median will be (71+ 87) / 2 = 79
A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.
Therefore, the correct answer is option A. The mean is less than the median.
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The complete question is:
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
HELP NEED ANSWERS QIUCKLY! WILL GIVE BRAINLEST!
1. What is the difference between arithmetic and geometric?
2. Which formulas are used for each? Explain ratio and difference.
3. Given 4, 8, 16, 32 identify the next term and if its a ratio or difference
4. Explain the steps in using the sigma notation.
Answers
Answer:
Arithmetic => each new term differs from the previous term by a fixed amount
an = a1 + d (n − 1)
Geometric => each element after the first is obtained by multiplying the previous number by a constant factor
an = a1 (r)^(n − 1)
4,8,16,32 the difference is not fixed so it is a geometric so it is ratio
the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64
To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.
if you also want the sum of them
arithmetic -> (n/2)(a1+an)
geometric -> (a1*(1-r^n))/(1-r) or
when the sequence is infinite you can use a1/(1-r)
Step-by-step explanation:
Arithmetic => 1,3,5,7,9,11,13,15....
Geometric => 1,2,4,8,16,32,64....
Find the total surface area.
Answers
Answer: 1308m
Step-by-step explanation:
Top and Bottom: 19 x 16 x 2 = 608
Sides: 16 x 10 x 2 = 320
Front and Back: 19 x 10 x 2 = 380
608 + 320 + 380 = 1308
Mitch throws a baseball straight up in the air from a cliff that is 95 ft high. The initial velocity is 95 /ftsec. The height (in feet) of the object after t sec is given by =ht+−19t2+95t95. Find the time at which the height of the object is 114 ft. Round your answers to two decimal places.
Answers
The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds
How to find the height of a projectile?We are given;
Height of cliff = 95 ft
Initial velocity of throw = 95 ft/s
The height (in feet) of the object after t sec is given by;
h(t) = −19t² + 95t + 95.
Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;
114 = −19t² + 95t + 95.
Subtract 114 from both sides to get;
−19t² + 95t + 95 = 0
Using quadratic formula, we have;
t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)
t = [-95 ± √(16245)]/-38
t = (-95 ± 127.4559)/(-38)
t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38
t = 5.85 s or -0.85
Time cannot be negative and so t = 5.85 seconds
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=
Use the Fundamental Counting Principle to solve.
A television programmer is arranging the order that three movies will be seen between the hours of 6 P.M. and 12
A.M. Two of the movies have a G rating, and they are to be shown in the first two time blocks. One of the movies is
rated NC-17, and it is to be shown in the last of the time blocks, from 10 P.M. until 12 A.M. Given these restrictions,
in how many ways can the three movies be arranged during the indicated time blocks?
The number of different ways the three movies can be arranged during the indicated time blocks is.
(Type a whole number.)
Answers
[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]
[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]
cual es el valor de x+5=7
Answers
Answer: x = 2
Work Shown:
x+5 = 7
x+5-5 = 7-5
x = 2
Subtract 5 from both sides to isolate x. This is to undo the plus 5.
What is the common denominator of x+5/x+8=1+6/x+1?
Answers
Answer:
(x+8) (x+1)
Step-by-step explanation:
To find the common denominator, we need to find the least common multiple of the terms in the denominator
(x+8) from the first term
(1) from the second term
(x+1) from the third term
The least common denominator is
(x+8) (1)(x+1)
Simplifiying
(x+8) (x+1)
please help! will give brainliest to whoever answers
maths functions
Answers
Answer:
1. f(x) is reflected across the x-axis
2. f(x) is translated 1 unit up
3. f(x) is vertically scaled by a factor of 2
4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2
5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down
6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up
Solving question:
(1) [tex]g(x) = -f(x)[/tex]
This graph has been reflected in the x axis. Equation: [tex]\sf g(x) = -\dfrac{2}{x}[/tex]
(2) [tex]g(x) = f(x) + 1[/tex]
Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]
(3) [tex]g(x) = 2f(x)[/tex]
This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]
(4) [tex]g(x) = -2f(x)[/tex]
This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]
(5) [tex]g(x) = 3f(x) - 1[/tex]
This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]
(6) [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]
This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]
Suppose f(x) = x2. What is the graph of g(x) = f(4x)?
Answers
[tex]g(x)=f(4x)=(4x)^2 = 16x^2[/tex]
The graph is shown in the attached image.
(4x + 5) - (2x - 3)
Answers
Answer:
2x + 8
Step-by-step explanation:
(4x + 5) - (2x - 3)
4x + 5 - 2x + 3
2x + 8
Answer: 2x+8
Step-by-step explanation:
4x+5-2x+3
=2x+8
Find the savings plan balance after 18 months with an APR of 5% and monthly payments of $200.
Answers
The savings plan balance after 18 months is $3,730.38
What is an ordinary annuity?
An ordinary annuity means that periodic savings are made at the end of each period unlike an annuity due where payments are made at the beginning of each period.
To determine the savings plan balance after 18 months, we need to make use of the future value formula of an ordinary annuity provided below:
FV=monthly payment*(1+r)^N-1/r
FV=future value after 18 months=unknown
monthly payment=$200
r=monthly interest rate=5%/12=0.00416666666666667
N=number of monthly payments in 18 months=18
FV=$200*(1+0.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.07771621094479000-1)/0.00416666666666667
FV=$200*0.07771621094479000/0.00416666666666667
FV=$3,730.38
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ASAP help me with this PLEASE
Answers
Answer:
98 degrees
Step-by-step explanation:
In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.
Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"
So using all the known values we can set up the following equation:
[tex]2x+64+100=360[/tex]
Simplify on the left side
[tex]2x+164=360[/tex]
Subtract 164 from both sides
[tex]2x=196[/tex]
Divide both sides by 2
[tex]x=98[/tex]
Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.
Please help!
(02.01 HC)
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y − 1) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments. (10 points)
Answers
Using translation concepts, it is found that:
The new coordinates of A' are: (5,0).The new coordinates of B' are: (5,2).The new coordinates of C' are: (9,2).The new coordinates of D' are: (9,0).Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule applied for each vertex of the rectangle is given as follows:
(x,y) -> (x + 7, y - 2).
The new coordinates of A' are given as follows:
(-2 + 7, 2 - 2) = (5,0).
The new coordinates of B' are given as follows:
(-2 + 7, 4 - 2) = (5,2).
The new coordinates of C' are given as follows:
(2 + 7, 4 - 2) = (9,2).
The new coordinates of D' are given as follows:
(2 + 7, 2 - 2) = (9,0).
Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.
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I, so confused please help me asap!
Answers
Quadrilaterals are plane shapes that are bounded by four straight sides. Thus, the required answers to the questions are:
46. True. Other examples include kites, rhombus, etc.
47. False.
46. When a plane shape is bounded by four straight sides of equal or different lengths, it is called a quadrilateral. Examples include trapezium, kite, rhombus, rectangle, square, etc. Each of these examples has individual properties.
Thus the required answer to question 46 is; True. It can be observed that with respect to their individual properties, other quadrilaterals which have a pair of opposite angles to be equal include: kite, rectangle, rhombus, etc.
47. A ray segment is a given line that points or heads in a specific direction. So that the direction in which the ray moves is very important.
Thus in the given question, the required answer is; False. This is because the two given rays are moving in opposite directions. Though the two rays may have the same length of the segment.
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Answers
The possible rational roots of the given equation are 1 and -3
Solving polynomial equationsFrom the question, we are to determine all the possible rational roots of the given equation
The given equation is
x⁴ -2x³ -6x² +22x -15 = 0
To determine the rational roots, we will test for values that make the equation equal to zero
Test for -1(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15
1 + 2 - 6 - 22 -15
= -40
∴ -1 is not a root of the equation
Test for 1(1)⁴ -2(1)³ -6(1)² +22(1) -15
1 - 2 - 6 + 22 -15
= 0
∴ 1 is one of the roots of the equation
Test for -2(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15
16 + 16 - 24 - 44 -15
= -51
∴ -2 is not a root of the equation
Test for 2(2)⁴ -2(2)³ -6(2)² +22(2) -15
16 - 16 - 24 + 44 -15
= 5
∴ 2 is not a root of the equation
Test for -3(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15
81 + 54 - 54 -66 -15
= 0
∴ -3 is one of the roots of the equation
Test for 3(3)⁴ -2(3)³ -6(3)² +22(3) -15
81 - 54 - 54 + 66 -15
= 24
∴ 3 is not a root of the equation
The other roots of the equation are irrational roots.
Hence, the possible rational roots of the given equation are 1 and -3
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Figure ABCD Is a kite. Find x
Answers
Answer:
x = 8
Step-by-step explanation:
Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.
SetupThe measure shown is equal to the angle measure of 90°.
14x -22 = 90
SolutionWe can solve this 2-step linear equation in the usual way.
14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone
x = 112/14 = 8 . . . step 2, divide by the coefficient of x
The value of x is 8.
What is The solution to -122 < -3(-2 - 8x) - 8x
A. x<8
B. x<-2
C. x>5
D. x>-8
Answers
Answer:
D.
Step-by-step explanation:
We can solve by simply isolating x:
[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]
You can check by plugging in any value greater than -8
-122<-3(-2-8(-7))-8*-7
-122<-3(-2+56)+56
-122<-3(54)+56
-122<-162+56
-122<-106
P=2(L+W) Solve for W
Answers
That should be the answer
Answer:
W = (P -2L)/2
Step-by-step explanation:
P = 2(L + W) Distribute the 2
P = 2L + 2W Subtract 2L from both sides
P - 2L = 2W Divide both sides by 2
(P-2L)/2 = W
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a
Answers
The best sampling strategy would be a stratified sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.
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The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answers
Answer:
Step-by-step explanation:
The average of six positive integers starting with a is equal to b. What is the average of five consecutive integers ending with b?
a)a+1
b)a-1
C)a+2
d)a+3
e)a+4
Answers
The average of the five consecutive numbers ending with b in discuss when expressed in terms of a is; Choice D; a+3.
What is the average of five consecutive integers ending with b?First, since it was given in the task content that the average of six positive consecutive odd integers starting with a is equal to b, it therefore follows that;
(a+a+2+a+4+a+6+a+8+a+10)/6 = b
6b=6a+30
b=a+5
Also, let the average of the consecutive intergers ending with b be denoted by; x.
(b+b-1+b-2+b-3+b-4)/5 = x
=(5b-10)/5
=b–2
The average, x=b – 2 (where b = a-5)
Ultimately, the value of the required average is; = a+5-2 = a+3.
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laura spends 4 hours reading a book that is 76 pages long. what is the average number of pages she read per hour?
Answers
The average number of pages she reads per hour is 19 pages per hour
How to determine the average number of pages she read per hour?The given parameters are:
Number of pages = 76 pages
Number of hours = 4 hours
The average number of pages she reads per hour is calculated using the following formula
Average = Number of pages/Number of hours
Substitute the known values in the above equation
Average = 76 pages/4 hours
Evaluate the quotient
Average = 19 pages per hours
Hence, the average number of pages she reads per hour is 19 pages per hours
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Answers
The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
How to illustrate the information?From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.
Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.
This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
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Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from. If no meal is repeated, how many different meal arrangements are possible?
Answers
Considering the definition of combination, if no meal is repeated, 210 different meal arrangements are possible.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following formula is applied:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.
Different meal arrangementsJoseph is planning dinners for the next 4 nights. There are 10 meals to choose from and no meal is repeated.
So, you know that:
m= 10n= 4Replacing in the definition of combination:
[tex]C=\frac{10!}{4!(10-4)!}[/tex]
Solving:
[tex]C=\frac{10!}{4!6!}[/tex]
[tex]C=\frac{3,628,800}{24x720}[/tex]
[tex]C=\frac{3,628,800}{17,280}[/tex]
C= 210
Finally, if no meal is repeated, 210 different meal arrangements are possible.
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find the positive square roots by division method of 151,321
Answers
The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.
What are the square roots of 151,321 by means of division method?It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.
Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.
Hence, the positive square root of the number 151,321 is; 389.
Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.
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