It will take 38 seconds for the sound to reach you
Explanation
Step 1
Let
speed of sound: 767.269
speed of ligth : 670616629 mph
also
[tex]\begin{gathered} \text{speed = }\frac{dis\tan ce}{\text{time}} \\ so \\ \text{time}=\frac{dis\tan ce}{\text{speed}} \end{gathered}[/tex]Step 2
a)hear the thunder
let
distance =8.1 miles
time=t
speed = 767.269 mph
replace
[tex]\begin{gathered} \text{time}=\frac{dis\tan ce}{\text{speed}} \\ =\frac{8.1miles}{767.269\text{ }\frac{\text{m}}{h}} \\ t=0.105\text{ hours} \end{gathered}[/tex]Step 2
we have the time in hours, the question is asking for how many seconds, so we need to convert the hours into seconds
[tex]1\text{ hour = 3}600\text{ sec}[/tex]hence
[tex]0.105\text{ hour}\cdot(\frac{3600\text{ sec}}{1\text{ hour}})=38\text{ sec}[/tex]therefore,the answer is
It will take 38 seconds for the sound to reach you
I hope this helps you
Sparks garden is a shape of a trapezoid in the dimension are shown below I got in your needs to spread fertilizer over the flower beds each bag of fertilizer he uses covers 240 m^2. would be the number of bags of fertilizers?
ANSWER:
12 bags of fertilizers are needed
STEP-BY-STEP EXPLANATION:
In this case we must calculate the area of the garden that has a trapezoid shape by means of the following formula:
[tex]A=\frac{B_1+B_2}{2}\cdot h[/tex]Replacing:
[tex]\begin{gathered} A=\frac{70+40}{2}\cdot50 \\ A=2750 \end{gathered}[/tex]Now to calculate the number of bags, we must divide the total area by the area covered by each bag of fertilizer, just like that:
[tex]\#b=\frac{2750}{240}=11.46\cong12[/tex]Find the surface area using the net. HELPP I have no idea how to do this please I need the steps if possible :(
surface area of cylinder=2 pi r h + 2 pi r x r
r=5
h=3
S=2x3.14x3x5 + 2x3.14 x5x5
S=251.33 sq.units
circle:
Area of circle =pi rxr
r=5
A=3.14x5x5
A=78.5 sq.units
surface area of cube =6a^2
a=2
a^2=4
S=6x4
S=24 sq.units
Issac factored 8x2−20x−12 to (8x+4)(x−3) and claims his answer is correct because his factored solution simplifies back to the original quadratic expression. Is Issac correct? Why or why not?
Given the equation :
[tex]8x^2-20x-12[/tex]The factor of the equation will be as following:
[tex]\begin{gathered} 8x^2=8x\cdot x\text{ or 4x }\cdot\text{ 2x} \\ 12=6\cdot2=4\cdot3 \end{gathered}[/tex]So, we will choose the numbers whose sum of multiplication = 20
So, the factor will be :
[tex]\begin{gathered} 8x^2-20x-12=(8x+4)(x-3) \\ or \\ 8x^2-20x-12=(4x+2)(2x-6) \end{gathered}[/tex]the factor of the equation should be as following :
[tex]8x^2-20x-12=4(2x+1)(x-3)[/tex]So, the answer of the student is not correct because he did not make 4 as a common
what is the slope formula of (-4,12) and (5,9) ?
what is the slope formula of (-4,12) and (5,9) ?
Applying the formula
m=(9-12)/(5+4)
m=-3/9
m=-1/3
therefore
the slope is -1/3what is the image of -1 - 5 after a dilation by a scale factor of 5 centered at the origin
the Given data
*The given point is (-1, -5)
*The given scale factor is 5
The image of -1 - 5 after dilation by a scale factor of 5 centered at the origin is given as
[tex](-1,-5)=(-1\times5,-5\times5)=(-5,-25)[/tex]Thus, the image after dilation by a scale factor of 5 centered at origin is (-5, -25)
Convert 2/3 to a decimal
The given expression is : 2/3
i.e Divisor = 3 and dividend = 2
Answer : 2/3 = 0.666
What is the area of a square if it is 216 inches in cubes? Please help me
In order to calculate the area of a square, which make part of a cube. You use the following formula:
A = a²
where a is the length of the side of the square and A is the area.
Then, you have to calculate the value of a. To do that, you use the information abou the volume of the cube and you use the following formula:
V = a³ solve for a by applying cubic root both sides
³√V = a replace V = 216 in³
a = ³√V
a = ³√(216 in³)
a = 6 in
Then, the length of the side of the square is 6 inches.
Next, you replace the value of a in the formula for the calculation of the area:
A = a²
A = (6 in)²
A = 36 in²
Hence, the are of the square is 36 in²
how many variations of the salad can you make containing at least 3 vegetables.
There are 7 options for the vegetables, and we can only pick 3. The number of variations is determined by
[tex]\binom{7}{3}=\frac{7!}{3!(7-3)!}=35[/tex]Therefore, there are 35 variations
two integers have a sum of 0 and a difference of 32. what are the integers?
Answer:
16 and -16
Explanation:
Let's call x the first number and y the second number.
If they have a sum of 0, we can write that:
x + y = 0
On the other hand, if the difference is 32, we can write the equation:
x - y = 32
Now, we have the system of equations:
x + y = 0
x - y = 32
We can add both equations to get:
x + y = 0
x - y = 32
2x + 0 = 32
Then, we can solve for x:
2x = 32
2x/2 = 32/2
x = 16
Finally, we can replace x by 16 and calculate the value of y as:
x + y = 0
16 + y = 0
16 + y - 16 = 0 - 16
y = -16
Therefore, the integers are x = 16 and y = -16
Prove AD= 3AB show exact steps to solve use algebraic terms for each step " Distributive property or Associative Multiplicative property" as of that
The question is to prove that
[tex]AD=3AB[/tex]From the diagram in the question, we can deduce that
[tex]AD=AB+BC+CD\text{ (TOTAL DIsTANCE FOR THE LINE)}[/tex]Also given from the question, we have
B is the midpoint of AC, that is
[tex]AB=BC(\text{ B bisects AC into two equal parts)}[/tex]Also given from the question, we have
C is the midpoint of BD, that is
[tex]BC=CD\text{ ( C bisects BD into two equal parts)}[/tex]Therefore,
since BC=CD ,and BC=AB then,
[tex]CD=AB\text{ (THE LINE IS DIVIDED INTO EQUAL SEGMENTS)}[/tex]By substituting the values of BC and CD in the total distance for the line , we will have
[tex]\begin{gathered} AD=AB+BC+CD \\ AD=AB+AB+AB \\ AD=3AB\text{ (AD IS 3 times the length of AB because the line is divided into equal lengths)} \\ \text{PROVED} \end{gathered}[/tex]AN O GEOMETRY Area involving rectangles and triangles A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer. Explanation mm Check 10m 7m 8m 6m 0 8 08 E X m² S m³ 1/5 ?
Given:
The sides of rectangle isl
[tex]\begin{gathered} l=10m \\ w=7m \end{gathered}[/tex]The sides of the triangle is
[tex]\begin{gathered} a=8m \\ b=6m \end{gathered}[/tex]Required:
To find the area of the shaded region.
Explanation:
The area of the triangle is
[tex]\begin{gathered} A=\frac{ab}{2} \\ \\ =\frac{8\times6}{2} \\ \\ =24m^2 \end{gathered}[/tex]Now the area of the rectangle is
[tex]\begin{gathered} A=lw \\ \\ =10\times7 \\ \\ =70m^2 \end{gathered}[/tex]The area of the shaded region is = Area of the rectangle - Area of the triangle.
[tex]\begin{gathered} =70-24 \\ =46m^2 \end{gathered}[/tex]Final Answer:
The area of the shaded region is
[tex]46m^2[/tex]find the volume of the cylinder. find the volume of the entire satellite.
Answer: the volume of the body is1590.4m^3
This body is composed of a cillinder and two hemisferes. The two hemispheres forms an entire sphere, so we can calculate the volume of the cillinder and the volume of the sphere and add them up
Volume of the cillinder:
[tex]\text{Vc}=\pi r^2h=\pi\cdot(4.5m)^2\cdot19m=1208.7m^3[/tex]Volume of sphere:
[tex]Vs=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(4.5m)^3=381.7m^3[/tex]diameter=2*r so the radius is half the lenght of the diameter
now we add them up
[tex]1208.7m^3+381.7m^3=1590.4m^3[/tex]The angular velocity of a point on a circle with radius of 13 feet is 14pi radians per second. Find the speed of the point on the circle.
Given:
The angular velocity of a point on a circle with radius of 13 feet is 14pi radians per second.
Required:
Find the speed of the point on the circle.
Explanation:
The speed is the angular in rad/sec times times the radius
[tex]\begin{gathered} =14\times\pi\times13 \\ =182\times\pi \\ =571.48 \end{gathered}[/tex]Answer:
Hence, option
I am having trouble graphing this equation, I know the answer but am having trouble graphing it
Two points define a line. Then, we can take two values of x and replace them in each equation to get their respective y-coordinates.
Equation 1[tex]\begin{gathered} \text{If }x=2 \\ -2x-y=0 \\ -2(2)-y=0 \\ -4-y=0 \\ \text{ Add y from both sides of the equation} \\ -4-y+y=0+y \\ -4=y \\ \text{ Then, the line passes through the point (2,-4)} \end{gathered}[/tex][tex]\begin{gathered} \text{If }x=-3 \\ -2x-y=0 \\ -2(-3)-y=0 \\ 6-y=0 \\ \text{ Add y from both sides of the equation} \\ 6-y+y=0+y \\ 6=y \\ \text{ Then, the line passes through the point (-3,6)} \end{gathered}[/tex]Now we can graph and connect the points to obtain the graph of this line:
Equation 2[tex]\begin{gathered} \text{If }x=0 \\ x-y=3 \\ 0-y=3 \\ -y=3 \\ \text{ Multiply by -1 from both sides of the equation} \\ -y\cdot-1=3\cdot-1 \\ y=-3 \\ \text{ Then, the line passes through the point (0,-3)} \end{gathered}[/tex][tex]\begin{gathered} \text{ If }x=1 \\ x-y=3 \\ 1-y=3 \\ \text{ Subtract 1 from both sides of the equation} \\ -y=2 \\ \text{ Multiply by -1 from both sides of the equation} \\ -y\cdot-1=2\cdot-1 \\ y=-2 \\ \text{ Then, the line passes through the point (1,-2)} \end{gathered}[/tex]Now we can graph and connect the points to obtain the graph of this line:
Finally, the solution of the system is the point at which the lines intersect:
Therefore, the solution of the system is
[tex]\begin{gathered} \boldsymbol{x=1} \\ \boldsymbol{y=-2} \end{gathered}[/tex]37) For which of the following values of L will the line whose equations are 2x + 3y = 8 and 6x *y=L be parallel?I.L L = 3
2x + 3y = 8
3y = 8 - 2x
y = 8/3 - 2/3x
6x + *y = L
*y = L - 6x
y = L/* - 6/* x
-6/* = - 2/3 in order to both lines be parallel
So * = 9
2x + 3y = 8
6x + 9y = L
L can have any of the three values I, II and III
A construction company plans to build houses. •The company will use 23 1/2 acres of land to build houses.•Each house will be built on a 1/4 acre lot.how many lots will the company have to build houses on?A.94B.48C.24D.6
94 (option A)
Explanation:Number of acres of land to build house = 23 1/2
In mixed fraction = 47/2
1 house = 1/4 acre lot
1 acre = 4 lots
47/2 acres = x
cross multiply:
x(1) = 4(47/2)
x = 2(47)
x = 94
The company will build houses on 94 lots (option A)
(1 point) The lifetime of a certain type of TV tube has a normal distribution with a mean of 57 and a standard deviation of 6months. What proportion of the tubes lasts between 58 and 60 months?
ANSWER:
12.4%
STEP-BY-STEP EXPLANATION:
Given:
Mean (μ) = 57
Standard deviation (σ) = 6
We can determine the percentage as follows:
[tex]\begin{gathered} P(58\leq x\leq60)=\left(\frac{60-\mu}{\sigma}\right)-\left(\frac{58-\mu}{\sigma}\right) \\ \\ \text{ We replacing:} \\ \\ P\left(58\le\:x\le60\right)=P\left(\frac{60-57}{6}\right)-P\left(\frac{58-57}{6}\right) \\ \\ P\left(58\le\:x\le60\right)=P\left(\frac{3}{6}\right)-P\left(\frac{1}{6}\right) \\ \\ P\left(58\le\:x\le60\right)=P\left(0.5\right)-P\left(0.17\right) \\ \end{gathered}[/tex]Determine these values with the help of the normal table, like this:
[tex]\begin{gathered} P\left(58\le\:x\le60\right)=0.6915-0.5675 \\ \\ P\left(58\le\:x\le60\right)=0.124=12.4\% \end{gathered}[/tex]Verify that the equation is an identity sec X - COS X= sin x tan x To verify the identity, start with the more complicatad side and transfom it to look like the other side. Choose the co séc X-COS X COS X Use a common denominator to perform the subtraction. Separate the expression into two factors = sin x tan x
You have the following equation:
secx - cosx = sinxtanx
In order to verify the previous identity, you show that the left side is equal to the right side. You proceed as follow:
secx - cosx = 1/cosx - cosx
to get the same denominators multiply by cosx/cosx in the second term:
1/cosx - cos²x/cosx
add the homogeneus fractions:
(1 - cos²x)/cosx
use the identity sin²x + cos²x = 1 => 1 - cos²x = sin²x
sin²x/cosx
write sin²x as sinxsinx
(sinx)(sinx/cosx)
separate the expression into two factors by replacing sinx/cosx = tanx
(sinx)(tanx)
Then, the given equation is an identity and it has been demonstrated that
secx - cosx = sinx tanx
12. Prove that, for any integer 2 1n?(n + 1)21² + 2 + 3 + ... + n° =
Answer:
Explanations:
Answer:
A tour bus is used to drive people on tours around New York City. The tour bus holds at most 35passengers. Which inequality shows this, using p for passengers?P35P. 35
ANSWER:
[tex]p\le35[/tex]STEP-BY-STEP EXPLANATION:
According to the statement we can determine that the tour bus can only have 35 people or less, therefore the inequality would be:
[tex]p\le35[/tex]Write the coordinates of the vertices after a translation 2 units right and 3 units down.101UTRS*-1001010R(-4, 3) R'OS(0,3) ► SCTO, 9) T'IU(-4, 9) - U'(
Translation of
2 units right ,then x'= x + 2
3 units down , then y'= y-3
THEN , new coordinates for vertices are
For U = (x,y) = (-4,9) transforms in U' = (-4+2,9-3)= (-2,6)
For T= (x,y)= ( 0,9) transforms in T'= (0+2, 9-3) = (2,6)
For R= (x,y)= (-4,3). Transforms in R'= (-4+2, 3-3)= (-2,0)
For S= (x,y)= ( 0,3). Transforms in S'= ( 0+2, 3-3) = (2, 0)
Kristina invests a total of $7,500 in two accounts paying 4% and 12% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $500.00.$ was invested at 4% and$ was invested at 12%.Submit QuestionQuestion 3
ANSWER:
$5000 was invested at 4% and $2500 was invested at 12%.
STEP-BY-STEP EXPLANATION:
We have that she has 7500 and invests an unknown amount, we will call x at 4%, then she has 7500-x to invest at 12%.
Therefore, we can plan the following equation:
[tex]0.04\cdot x+0.12\cdot\mleft(7500-x\mright)=500[/tex]Solving for x:
[tex]\begin{gathered} 0.04x+900-0.12x=500 \\ -0.08x=500-900 \\ x=\frac{-400}{-0.08} \\ x=5000 \end{gathered}[/tex]Therefore she, 5000 $ at 4%, to calculate at 12% it would be:
[tex]7500-5000=2500[/tex]It means that at 12% she invested $ 2500
Santa read 1/5 of the book before lunch & 3/5 after lunch. What part of the book has he read?
Given that:
Part of the book Santa read before lunch = 1/5
Part of the book Santa read after lunch = 3/5
Part of the book Santa has read
= Part of the bok Santa read before lunch + Part of the book Santa read after lunch
[tex]\begin{gathered} =\frac{1}{5}+\frac{3}{5} \\ =\frac{1+3}{5} \\ =\frac{4}{5} \end{gathered}[/tex]alyssas family is staying at the lake house this weekend for a family reunion. She is in charge of making homemade pancakes for the entire group . The pancakes mix requires 2 cups of flour for every 10 pancakes write a ratio to show the relationship between the number of cups of flour and the number of pancakes made. PLEASE HELP THIS IS DO IN 20 MINUTES
We are told that Alyssa needs 2 cups of flour for every 10 pancakes.
The ratio between cups and pancakes will be as follows:
[tex]\text{ratio}=\frac{\text{cups of flour}}{pancakes}[/tex]Which, is we substitute our values we get:
[tex]\text{ratio}=\frac{2}{10}[/tex]As you can see, the ratio is a division between the two indicated values.
We can simplify the fraction of the answer if we divide both 2 and 10 by 2:
[tex]\text{ratio}=\frac{2}{10}=\frac{1}{5}[/tex]Answer:
the ratio is 1/5 (sometimes represented also as 1:5)
39. The quotient of twice a number plus 8 and 3 is greater than or equal totwice the number less 10.Which Inequality and solution accurately solves for the number?
SOLUTION
Given:
39. The quotient of twice a number plus 8 and 3 is greater than or equal to
twice the number less 10.
Which Inequality and solution accurately solves for the number?
[tex]Let\text{ the number be x;}[/tex][tex]\frac{2x+8}{3}\ge2x-10[/tex]
To solve for the number;
[tex]\begin{gathered} \frac{2x+8}{3}\ge2x-10 \\ \text{ multiply both sides by 3;} \\ 2x+8\ge6x-30 \\ subtract\text{ 6x from both sides;} \\ 2x-6x+8\ge6x-6x-30 \\ -4x+8\ge-30 \\ -4x\ge-38 \\ \frac{-4x}{-4}\leq\frac{-38}{-4} \\ x\leq9.5 \end{gathered}[/tex]Final answer:
[tex]x\leq9.5[/tex]
What is the total number of lines of symmetry in a square?A. 3 or moreB. 2C. 0D. 1
A line of symmetry is the line into two halves that match exactly.
In a square, the first two line of symmetry crosses through each diagonal. The other two are the horizontal and vertical lines that cross through the middle of the square.
Hence, a square has 3 or more lines of symmetry. The answer is option A
A books had a length of 10 inches & width of 10 inches. What is the area of the book?
Step 1:
A book of equal length and width has a shape of a square
Step 2:
Write the formula for the area of a square.
[tex]\text{Area of a square = L}^2[/tex]Step 3:L
L = 10cm
[tex]\begin{gathered} \text{Area of a square = 10}^2 \\ \text{= 100 in}^2 \end{gathered}[/tex][tex]\begin{gathered} F\text{inal answer} \\ Areaofthebook=100in^2 \end{gathered}[/tex]can you please help me
Each topping pizza will have one of crust, sauce and a choice of toppings.
Hence, the number of single toppings that can be made is
2 x 3 x 9 = 54. Option D.
divide 4 x 2/3 + 3 / X - 1
Given data:
The firts expression given is 4x+2/3.
The second expression given is x-1.
[tex]\begin{gathered} (4x+\frac{2}{3})\times\frac{1}{x-1}=\frac{12x+2}{3(x-1)} \\ =\frac{12x-12+14}{3(x-1)} \\ =\frac{12(x-1)+14}{3(x-1)} \\ =4+\frac{14}{3(x-1)} \end{gathered}[/tex]Thus, when the given term is divided we get 14/3 as remainder.
To make a model of the Guadalupe Tiver bed, hermonie used 1inch of clay for 5 miles of the rivers actual length. His model river was 50 inches long how long is the Guadalupe river ?
We have a model at scale of the river.
The scale is 1 inch in the model = 5 miles in the actual river.
We know that his model was 50 inches long, so we can calculate the actual length as:
[tex]L=50in\cdot\frac{5mi}{1in}=250mi[/tex]NOTE: we multiply the length of the model by the scale, in a way that the units of the model cancel each other (inches divided by inches, in this case). If we we want to find the actual length, the scale of the model goes in the denominator and the scale of the actual length goes in the numerator.
Answer: the actual length of the river is 250 miles.