The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.
To determine the total distance he traveled you have to add both distances:
[tex]1\frac{3}{4}+\frac{1}{3}[/tex]To solve this sum, add the fractions first and then add the result to the whole number:
- Add both fractions:
[tex]\frac{3}{4}+\frac{1}{3}[/tex]To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:
[tex]\frac{3\cdot3}{4\cdot3}+\frac{1\cdot4}{3\cdot4}=\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}=\frac{13}{12}[/tex]The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:
- Solve the division:
[tex]13\div12=1.08\bar{3}[/tex]The mixed number will have the whole number "1".
- To express the decimal value as a fraction, multiply it by 12
[tex]0.08\bar{3}\cdot12=1[/tex]The result is the numerator of the fraction, and the denominator will be 12, so:
[tex]0.08\bar{3}=\frac{1}{12}[/tex]And the resulting mixed number is:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:
[tex]1+1\frac{1}{12}=2\frac{1}{12}[/tex]The distance he traveled from home to school is 2 1/12 km.
Which graph represents the solution of −2x≤4(x−6)?
Answer:
See attachments.
Step-by-step explanation:
Given inequality:
[tex]-2x\leq 4(x-6)[/tex]
Solve the inequality by first expanding the brackets:
[tex]\implies -2x\leq 4x-24[/tex]
Subtract 4x from both sides:
[tex]\implies -2x-4x\leq 4x-24-4x[/tex]
[tex]\implies -6x\leq -24[/tex]
Divide both sides by -6 (remembering to reverse the inequality sign as we are dividing by a negative number).
[tex]\implies \dfrac{-6x}{-6}\leq \dfrac{-24}{-6}[/tex]
[tex]\implies x\geq 4[/tex]
When graphing inequalities on a coordinate plane:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given inequality on a coordinate plane:
Draw a solid line at x = 4.Shade above the line (i.e. shade to the right of the line).(See attachment 1).
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle..Therefore, to graph the given inequality on a number line:
Place a closed circle at 4.Shade to the right of the circle.(See attachment 2).
Joe bought 8 comic books for $36. How much does 1 comic book cost?
Answer:
1 comic book costs $4.5
Explanation:
Given that 8 comic books cost $36
To know how much 1 comic book costs, let x be the cost of 1 comic book, then, we have:
8 comic books = $36
1 comic book = x
Then we have the equation
8x = 36
where we can solve for x
Divide both sides by 8
8x/8 = 36/8
x = 4.5
Therefore, 1 comic book costs $4.5
find the value of the expression 4d ÷ c when c=3and d=6 simplify your answer
Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
2. State two (2) values of θ (theta) to the nearest degree forsin θ = − 0. 966
To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input
[tex]\begin{gathered} \theta=\arcsin\left(x\right) \\ \\ \theta=\arcsin(-0.966) \\ \\ \theta=−75 \end{gathered}[/tex]The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°
Now to find the other value we will look at the symmetry in the trigonometric circle:
Then, the other value of theta will be
[tex]\begin{gathered} \theta_2=-75°-30° \\ \\ \theta_2=105° \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} \theta=-75° \\ \theta_2=-105° \end{gathered}[/tex]suppose s is between r and t use the segment addition postulate to solve for each variable RS equals 2z plus 6 St equals 4z - 3 RT = 5z + 12
If s is between r and t, then:
RS + ST = RT
Where RS = 2z + 6
ST = 4z - 3
RT = 5z + 12
So, we get:
(2z + 6) + (4z - 3) = 5z + 12
Solving for z, we get:
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
6z + 3 - 5z = 12
z + 3 = 12
z = 12 - 3
z = 9
Answer: z = 9
Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
Given the equation y = x (x - 3)(2x + 7), find the rational roots. Complete theexplanation.The rational roots are x =, and. I found my answers bygraphing the equation, then finding where the equation crossed the (select) ▼4'
ANSWER
[tex]0,3,-\frac{7}{2}[/tex]EXPLANATION
The roots are the x values where the equation intercepts the x-axis.
how can you obtain the points for the log below from its inverse?
Answer
Check Explanation
Explanation
The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.
Before we commence, the two laws of logarithms that we will be using is that
log₄ 4ᶜ = c (log₄ 4)
And
log₄ 4 = 1
So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.
when x = 1
f(x) = log₄ x
f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0
when x = 4
f(x) = log₄ x
f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1
when x = 16
f(x) = log₄ x
f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2
when x = 64
f(x) = log₄ x
f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3
Hope this Helps!!!
Finding Slope
HELP ME PLS
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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What is a feature of function g if g(x) = log (x-4) -8
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
If joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was joey from home?
The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
It is known that East and West are the opposite of each other.
So, 15 2/3 towards the east let's take it positively.
And 21 3/4 towards left let's consider it negative.
So, the distance from the home
⇒ | ( 15 + 2/3) - (21 +3/4) |
⇒ | 15 -21 + 2/3 - 3/4 |
⇒ | -6 + (8 - 9)/12 |
⇒ | -6 - 1/12 |
⇒ | -(6 +1/12) |
⇒ 6 1/12
Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".
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I need to write this equation that has a infinite number of solutions
2 (8x+4) -x =
Simplify the equation:
2(8x)+2(4) -x
16x +8 -x
15x +8
If both sides of the equation are equal o equivalent, there is an infinite number of solutions.
2 (8x+4) -x = 15x + 8
Slope =
y-intercept = (0,
Answer:
y intercept= (0,-3)
slope= 2/1 or simplified 2
Step-by-step explanation:
13х-17y+16z= 73
-11x + 15y + 17z= 61
46x+10y-30z = -18
The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4
What is a set of simultaneous equation?Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.
The linear system of three equations can be presented as follows;
13•x - 17•y + 16•z = 73...(1)
-11•x + 15•y + 17•z = 61...(2)
46•x + 10•y - 30•z = -18...(3)
The above system of equations can be solved using common multiples of the coefficients as follows;
Multiply equation (2) by 2 and equation (3) by 3 to get;
2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122
-22•x + 30•y + 34•z = 122...(4)3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54
138•x + 30•y - 90•y = -54...(5)Subtracting equation (4) from equation (5) gives;
138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176
138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176
160•x - 124•z = -176
40•x - 31•z = 44
[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]
Plugging in the value of z in equation (1) and (2) gives;
1043•x - 527•y + 704 = 73 × 31 = 2236...(6)
Which gives;
[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]
339•x + 465•y + 748 = 61 × 31 = 1891...(7)
Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;
[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]
Therefore; 221216•x - 442432 = 0
x = 442432 ÷ 221216 = 2
x = 2
y = (1043×2 - 1559)÷527 = 1
y = 1
z = (44 + 40×2) ÷ 31 = 4
z = 4
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A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week. X, and grade-point average, y. Shefound that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ý = -0.0579x + 2.9408(Round to the nearest hundredth as needed.)(Part b) Interpret the slope.For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0579 points, on average.(Part c) if appropriate, interpret the y-intercept.A. The grade-point average of a student who does not play video games is 2.9408.B. The average number of video games played in a week by students is 2.9408.C. It cannot be interpreted without more information.
exactly For sentence A "The grade-point average of a student who does not play video games is 2.9408" we can verify as follows:
That means this sentence "The grade-point average of a student who does not play video games is 2.9408" is true.
For sentence B "The average number of video games played in a week by students is 2.9408" is not exactelly correct because the average number of hours of video game played is not specified.
For sentence C "It cannot be interpreted without more information" let's look over an illustration.
We can see, we can interpret the y-intercept as the moment where x = 0 which means when the student does not play a video game. So this sentence is false.
I mean the correct sentence is sentence A.
When you are on the 2nd step of factoring this trinomial,you should be listing the factors of?
Given:
The trinomial equation is given as,
[tex]3v^2-4v-7[/tex]The objective is to choose the correct value for which the factors are to be obtained for factorization.
Explanation:
From the step 1, to perform the factorization the values of a and c has to be multiplied.
Then in step 2, the factors need to be calculated for the product of a and c.
Product of a and c :
The product of a and c will be,
[tex]a\times c=3\times7=21[/tex]Thus, factors are to be listed for the number 21.
Hence, option (1) is the correct answer.
Created by Cortin Lyons riables on Both Sides #3 2.12r – 14 = 8x + 16 12x – 14 = 6x + 16 as with Distributive Property
Problem N 2
we have
12x-14=8x+16
solve for x
subtract 8x both sides
12x-14-8x=8x+16-8x
4x-14=16
Adds 14 both sides
4x-14+14=16+14
4x=30
divide by 4 both sides
x=30/4
x=7.5
Problem N 4
we have
12x-14=6x+16
solve for x
subtract 6x both sides
12x-14-6x=6x+16-6x
6x-14=16
adds 14 both sides
6x=16+14
6x=30
divide by 6 both sides
x=30/6
x=5
Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]A company has developed a new deluxe AAA battery that is supposed to last longer than its regular AAA battery. However these new batteries are more expensive to produce. So the company would like to be convinced that they really do last longer. Based on years of experience, the company knows that its regular AAA batteries last lor 45 hours of continuous use. On average. The company selects an SRS Of 50 new batteries and uses them continuously until they are completely drained. The Sample mean lifetime is X =46.9 hours with a Standard deviation of S=4.6 hours A) Check for the conditions for the situation B) Calculate the test statistic for this situation C) What is the P value for this situation? D) What conclusion do you draw with 5% significance level? why? E) What type of error could you possibly make here? I
1 sample t-test
[tex]\mu=the\text{ true mean lifetime of new AAA batteries}[/tex][tex]\begin{gathered} H_0\colon\mu=45\text{ hours} \\ H_a\colon\mu>45\text{ hours} \end{gathered}[/tex][tex]n=50[/tex]B)
Calculating t test statistic
[tex]\begin{gathered} t=\frac{statistic-parameter}{s\tan dard\text{ deviation of statistic}} \\ t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \end{gathered}[/tex]Plugging in the values, we have:
[tex]\begin{gathered} t=\frac{\bar{x}-\mu_0}{\frac{s_x}{\sqrt[]{n}}} \\ t=\frac{46.9-45}{\frac{4.6}{\sqrt[]{50}}} \\ t=\frac{1.9}{0.6505} \\ t=2.9207 \end{gathered}[/tex]C)t test statistic = 2.9207
degrees of freedom = n - 1 = 50 - 1 = 49
Using a calculator, we can calculate the p-value.
[tex]p-\text{value}=0.002633[/tex]D)Since p value is less than significance level (p value < alpha), then we will reject H_0 and take the alternate hypothesis.
Thus the test suggests that the new batteries do last more than 45 hours.
E)
We could've done Type I error here.
Type I error or α: Reject the null when it’s true.
Draw a line connecting each sphere to its volume in terms of π and round it to the nearest tenth. (Not all of the values will be used.)
Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^3[/tex]N 1
we have
D=9 units
r=9/2=4.5 units
substitute
[tex]\begin{gathered} V=\frac{4}{3}\pi(4.5)^3 \\ V=121.5\pi\text{ unit3} \\ V=381.5\text{ unit3} \end{gathered}[/tex]N 2
we have
r=2 units
[tex]\begin{gathered} V=\frac{4}{3}\pi2^3 \\ V=10.6\pi\text{ unit3} \\ V=33.5\text{ unit3} \end{gathered}[/tex]N 3
we have
D=14 units
r=14/2=7 units
[tex]\begin{gathered} V=\frac{4}{3}\pi7^3 \\ V=457.3\pi\text{ unit3} \\ V=1,436\text{ unit3} \end{gathered}[/tex]N 4
we have
r=9 units
[tex]\begin{gathered} V=\frac{4}{3}\pi9^3 \\ V=972\pi\text{ unit3} \\ V=3,052.1\text{ unit3} \end{gathered}[/tex]prove the formula sin 3 A + sin A = 4 sin A cos2A
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
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Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
Question 8 > Find the area of the trapezoid shown below 9 19 18 21 23 I Question Help ve
288 u²
1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:
[tex]\begin{gathered} S=\frac{(B+b)h}{2} \\ S=\frac{(23+9)18}{2} \\ S=288 \end{gathered}[/tex]2) So that trapezoid has an area of 288 u²
Convert to fractional Notation 4 19/100
to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions
to do that we can multiply 4 and 1 by 100, like this:
[tex]\frac{4\cdot100}{1\cdot100}=\frac{400}{100}[/tex]now we can add the fractions
[tex]\frac{400}{100}+\frac{19}{100}=\frac{419}{100}[/tex]So the answer is: 419/100
The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR
#11 When you were born, your grandparents deposited $10,000 in a CD. for your college education. If theaccount earns 5% interest, compounded monthly, how much will be in the account for your collegeeducation?
Replacing with the values we already know, we have:
PV = 10,000
i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12
n = 18 years or 216 months
10,000 = FV * 0.4073
FV = 10,000/0.4073
FV = $ 24,551.93
It is very close to option D, where the term "about" is included.
complete the table to show the total change in the average mean daily in the price of for stocks over a five-day.
Answer: -$0.26, -$0.7, $0.65, and -$1.6
The number of days = 5
Average price = Total change in price / the number of days
For Stock A
Total change in price = -$1.30
Average price = - 1.30 / 5
Average price = -$0.26
STOCK B
Average change in price = -$0.14
From, Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.14 x 5
Total price = - $0.7
For stock C
Average price = 3.25 / 5
Average price = $0.65
Stock D
Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.32 x 5
Total price = - $1.6
The answer are -$0.26, -$0.7, $0.65, and -$1.6
A parallelogram has an area of 364.5 cm2. If the base is 27 cm, What is the height?
Answer:
Height = 13.5cm
Explanation:
The area of a parallelogram is obtained using the formula below:
[tex]\text{Area}=\text{Base}\times Height[/tex]Substituting the given values:
[tex]\begin{gathered} 364.5=27\times\text{Height} \\ \text{Height=}\frac{364.5}{27} \\ H\text{eight}=13.5\operatorname{cm} \end{gathered}[/tex]