Given the expression below,
Oh no! You have just discovered Superhero C is actually a villain! He plans toactivate an underwater volcano that is 50 miles away. Superhero A is goingto try to stop him.Suppose getting to the underwater volcano requires a combination ofrunning, flying, and swimming.Using the rates from Table 1, make a plan for how far each Superheroshould run, fly, and swim to make sure that Superhero A gets to the volcanobefore Superhero C and can save the world.Note: You must use all three modes of travel.
SOLUTION:
First, let's calculate for superhero C the villian.
Using the three modes of travelling,
He needs to cover a distance of 50 miles
If he:
i. Runs
1 mile in 2 minutes, Hence
50 miles will be in 100 minutes
ii) Flys
2 miles in 2 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
4 miles in 3 minutes, Hence
50 miles will be in 37.5 minutes
Next, let's calculate for superhero A.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
4 miles in 1 minute, Hence
50 miles will be in 12.5 minutes
ii) Flys
4 miles in 4 minutes, Hence
50 miles will be in 50 minutes
iii) Swims
3 miles in 1 minute, Hence
50 miles will be in 16.67 minutes.
Finally, let's calculate for superhero B.
Using the three modes of traveling,
He needs to cover a distance of 50 miles
If he:
i. Runs
5 miles in 1 minute, Hence
50 miles will be in 10 minutes
ii) Flys
7 miles in 2 minutes, Hence
50 miles will be in 14.29 minutes
iii) Swims
10 miles in 3 minutes, Hence
50 miles will be in 15 minutes.
I need help on this equationTo simplify each and state the excluded value.
To answer this question, we need to factor each of the polynomials as follows:
First Polynomial
[tex]x^2+4x+3[/tex]To factor it, we need to find two numbers:
a*b = 3
a + b = 4
These numbers are:
a = 3
b = 1
Therefore, we have:
[tex]x^2+4x+3=(x+1)(x+3)[/tex]A ladder, 510 cm long, leans against a building. If the angle between the ground and the ladder is 57 degrees, how far from the wall is the bottom of the ladder? Round to the nearest tenth
Let's use cosine function to find the distance between the wall and the bottom of the ladder:
[tex]\begin{gathered} \cos (\theta)=\frac{adjacent}{hypotenuse} \\ \cos (57)=\frac{x}{510} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=510\cdot\cos (57) \\ x=277.8\operatorname{cm} \end{gathered}[/tex]What is the perimeter of triangle XYZ? A. 17.1 cmB. 15.1 cmC. 13.1 cmD. 11.1 cm
The perimeter of the triangle XYZ is 15.1 cm.
The two given triangles are ΔUVW and ΔXYZ are similar.
In ΔUVW ∠U=36°
In ΔXYZ ∠Y = 72° and ∠Z = 72° , ∴ ∠X = 180° - (72+72)° = 36°
Hence in the two triangles we can assume that they are similar by AAA axiom of similarity
So the sides of the triangle XYZ will be
XY = 5.7 cm
YZ = 5.7 cm
ZX = 3.7 cm
Hence the perimeter = XY+YZ+ZX = 5.7 + 5. 7+ 3.7 = 15.1 cm
A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is referred to as its perimeter.
Perimeter calculations have many practical applications. The perimeter is the width of the fence required to completely enclose a yard or garden. The circumference, or perimeter, of a wheel or circle determines how far it will travel in one rotation.
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You are performing a left-tailed test with test statistic z = -2.329, find the p-value accurate to 4
decimal places.
p-value =
The p-value is 0.00993
What is critical value ?
The distribution's critical values are the points that have the same probability as your test statistic and are equal to the significance level. It is considered that these values are at least as extreme as those essential values.
The points with the property that the area under the density curve of the test statistic from those points to the tails is equal to can be readily represented as critical values:
Left-tailed test: The critical value to the left of the area under the density curve is equal to ;
Right-tailed test: The density curve's area under the right side of the critical value equals ; and
Two-tailed test: The total area is equal to since the area under the density curve from the left critical value to the left is equal to ∝/2 and the area under the curve from the right critical value to the right is equal to ∝/2 as well.
When z = -2.329
After left-tailed test the p-value from the graph is 0.00993
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Lynn is tracking the progress of her plant's growth. The plant is already 8 centimeters high. The plant grows 1.5 centimeters per day. Which function shows this relationship? y=8x+1.5y=1.5x+8y=9.5x
Given the information, we know that the plant is already 8 centimeters, therefore that would be our intercept with the y-axis (i.e. b = 8). Now, to find the slope, we have that on the first day the plant grows 1.5 centimeters, therefore for day 1, the plant is 9.5 centimeters high. With this observations we have the following:
[tex]\begin{gathered} \text{Given (0,8) and (1,9.5)} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{9.5-8}{1-0}=1.5 \\ m=1.5 \end{gathered}[/tex]Using the formula y=mx+b, we obtain the desired function:
[tex]\begin{gathered} y=mx+b \\ \Rightarrow y=1.5x+8 \end{gathered}[/tex]Therefore, the function that shows the relationship is y=1.5x+8
what is the name of the geometric figure that begins at a point and is a set of all points that make a never-ending straight path extending in only one direction?
hi.
to start this exercise, let's remember some definitions about the alternatives:
a. ray
distance between the center of the circle and a point on its circumference (one straight line)
b. vertex
is a point where two edges meet
c. angle
is formed by two semi-straights that come from the same origin
d. opposite rays
is the same definition of radius, only now it considers two rays: one and its opposite. joining a radius to its opposite, we get a straight line.
write an equation in slope intercept form for the line that passes through the given point and is perpendicular to the graph of the equation. (-4,2); y= -1/2x + 6
First of all we are going to find the slope perpendicular to the equation y = -1/2 x +6.
We need to remember that two slopes are perpendicular if its product is equal to -1. Like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_1=-\frac{1}{2}_{} \\ m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{1}{2}}=2 \\ m_2=2 \end{gathered}[/tex]Now, we find the equation of the line using the general form:
[tex](y-y_1)=m(x-x_1);\text{ }[/tex]m - slope
[tex](x_1,y1)=(-4,2)_{}[/tex]That was a point of the line, now:
[tex]\begin{gathered} (y-2)=2(x-(-4)) \\ y-2=2x+8 \\ y=2x+10 \end{gathered}[/tex]Finally, the equation of the line that passes through (-4,2) and is perpendicular to the equation y = -1/2x+6 is
y=2x+10
A person riding a ferris wheel takes 10 minutes to make one complete trip around thewheel. A function in the form y = A cos (Bt) + C can be used to model thissituation. Based on the information given, determine the values of B.
ANSWER
[tex]\frac{\pi}{300}[/tex]EXPLANATION
The function given is a cosine function:
[tex]A\cos (Bt)+C[/tex]From the function, B can be found as:
[tex]B=\frac{2\pi}{P}[/tex]where P represents the period of the function.
The period is given as 10 minutes (600 seconds), which means that we can find B:
[tex]\begin{gathered} B=\frac{2\pi}{600} \\ B=\frac{\pi}{300} \end{gathered}[/tex]That is the value of B.
Solve the system of linear equations using the graphing method. Use “no solution” and “infinitely many” when appropriate.
Given the system of equations:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]Let's solve the system using graphing method.
Let's plot both equations on a graph. The point where both lines meet.
• Equation 1:
Let's plot using 3 points.
Substitute random values of x and solve for y.
We have:
[tex]\begin{gathered} x=-4;\text{ y = }\frac{1}{2}(-4)+2=-2+2=0 \\ \\ x=0;y=\frac{1}{2}(0)+2=0+2=2 \\ \\ x=4;y=\frac{1}{2}(4)+2=2+2=4 \end{gathered}[/tex]For equation 1, we have the points:
(x, y) ==> (-4, 0), (0, 2), (4, 4)
Plot the points and connect the points with a straight line.
• Equation 2:
Let's create 3 points:
[tex]\begin{gathered} x=-2;y=\frac{1}{2}(-2)+1=-1+1=0 \\ \\ x=0;y=\frac{1}{2}(0)+1=0+1=1 \\ \\ x=2;y=\frac{1}{2}(2)+1=1+1=2 \end{gathered}[/tex]FOr equation 2, we have the points:
(x, y) ==> (-2, 0), (0, 1), (2, 2)
Now, plot the points and connect using a straight line.
We have the graph of both equations below:
From the graph, we can see that both lines do not meet at any point.
They are parallel lines,
Since they will not meet at any point, there is NO SOLUTION.
ANSWER:
No solution.
What is the domain of the cubic function f(x)= 9x³ + 2x-12 ?
GIVEN:
We are given the function below;
[tex]f(x)=9x^3+2x-12[/tex]Required;
To find the domain of the cubic function.
Step-by-step solution/explanation;
The domain of a function is the set of all input values (that is, x values) for which the function is defined.
For the function given, there is no constraint, which means the function is always true for any value of x.
Therefore,
ANSWER:
[tex]Domain=(-\infty,+\infty)[/tex]The domain is the set of all real numbers.
Option B
If the scale is 1 in: 4 yards, what’s the area of the actual right triangle?
To answer this question, first, we transform the base and the height from inches to yards.
Since the scale is 1 in : 4 yards, then:
[tex]\begin{gathered} 9\text{ in=36 yards,} \\ 6\text{ in=24 yards.} \end{gathered}[/tex]Substituting the above values in the formula for the area of a triangle, we get:
[tex]A=\frac{36\text{yards}\cdot24\text{yards}}{2}\text{.}[/tex]Simplifying the above result, we get:
[tex]A=\frac{864}{2}squareyards=432\text{ square yards.}[/tex]Answer:
[tex]A=432\text{ square yards.}[/tex]Nancy bought a pack of 10 cookies for her 3 children to share equally. How many cookies should each child get if the cookies are shared equally between the 3 children?
Given:
Total pack is 10.
Share divied in 3 children.
So each children share is:
[tex]\begin{gathered} 3\text{ total share is 10} \\ for\text{ each share}=\frac{10}{3} \\ =3.33 \end{gathered}[/tex]each children share is 3.33 cookies.
Find the scale factor of the two prisms, the ratio of their surface areas, and the ratio of theirvolumes. List the larger values first.6 cm8 cm9 cm10 cm12 cm15 cmScale FactorSurface AreasVolumesBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:Blank 6:
We will operate as follows:
*Scale factor:
We determine the scale factor using two respective sides, that is:
[tex]9x=6\Rightarrow x=\frac{6}{9}\Rightarrow x=\frac{2}{3}[/tex]So, the scale factor is 2 : 3.
*Surface area:
We determine the surface are of each prism:
[tex]S_{A1}=(9\cdot12)+2(\frac{15\cdot9}{2})+(12\cdot\sqrt[]{15^2+9^2})+(15\cdot12)\Rightarrow S_{A1}=(108)+(135)+(36\sqrt[]{34})+(180)[/tex][tex]\Rightarrow S_{A1}=423+36\sqrt[]{34}\Rightarrow S_{A1}=632.9142682\ldots[/tex][tex]S_{A2}=(6\cdot8)+2(\frac{6\cdot10}{2})+(10\cdot8)+(8\cdot\sqrt[]{6^2+10^2})\Rightarrow S_{A2}=(48)+(60)+(80)+(16\sqrt[]{34})[/tex][tex]\Rightarrow S_{A2}=188+16\sqrt[]{34}\Rightarrow S_{A2}=281.2952303\ldots[/tex]Now:
[tex](423+36\sqrt[]{34})x=188+16\sqrt[]{34}\Rightarrow x=\frac{188+16\sqrt[]{34}}{423+36\sqrt[]{34}}\Rightarrow x=\frac{4}{9}[/tex]So, the ratio of the surface areas is 4 : 9.
*Volume:
We determine the volume of each prism and proceed as before:
[tex]V_1=\frac{9\cdot15\cdot12}{2}\Rightarrow V_1=810[/tex][tex]V_2=\frac{6\cdot10\cdot8}{2}\Rightarrow V_2=240[/tex]Now:
[tex]810x=240\Rightarrow x=\frac{240}{810}\Rightarrow x=\frac{8}{27}[/tex]So, the ratio for the volumes is 8 : 27.
a Ford is traveling 20 miles per hour slower than a Buick. the Buick is traveling at a rate of 65 miles per hour.Let F = the speed of the Ford which formula would correctly calculate the speed of the ford?
The answer is: F - 20mph = 65mph
7. Write an equation that results when f(x) = 5^xhas been transformed by:a. Shifted to the left 2 and up 3b. Shifted right 3 and down 1
The given function is:
[tex]undefined[/tex]Please help will mark Brainly
Answer:
y = 4x + 3
Step-by-step explanation:
if you try plugging in the x on the table to the x in the equation you should get the answer under the column y to match up
Sondra Anderson was looking at a winter coat that regularly sells for $179.99. On the rack was a sign that read 25% off all winter coats. What will the sale price be of the coat that Sondra wants to buy?
Given:
The regular price of the coat = $179.99
Percent-off the regular price = 25%
To find:
The sales price of the coat
To determine the sales price of the cot, we need to first find the amount of discount
[tex]\begin{gathered} Discount\text{ = 179.99 }\times\text{ 25\%} \\ Discount\text{ = 179.99 }\times\text{ 0.25} \\ Discount\text{ = 44.9975} \end{gathered}[/tex]The sales price = Original price - discount
[tex]\begin{gathered} The\text{ sales price = 179.99 - 44.9975} \\ \\ The\text{ sales price = 134.9925} \\ \\ The\text{ sales price of the coat Sandra want to buy = \$134.99} \end{gathered}[/tex]Evaluate the expression (-4-4i) +(-8-11) and write the result in the form a + bi.The real number a equalsThe real number b equals
The answer is supposed to be in the form
[tex]a+bi[/tex]Therefore,
[tex](-4-4i)+(-8-1i)[/tex][tex]\begin{gathered} -4-4i-8-1i \\ \end{gathered}[/tex]combine like terms
[tex]-4-8-4i-1i[/tex]Finally,
[tex]-12-5i[/tex]a = -12
b = -5
A basket of fruits contains 50 mangoes and 30 orange. what percentage of the fruits are oranges?
The percentage of oranges is the basket of fruits is 37.5%.
According to the question,
We have the following information:
A basket of fruits contains 50 mangoes and 30 orange.
Now, we can easily find the number of oranges in this basket by following the given steps.
Total number of fruits in the basket = number of mangoes + number of oranges
Total number of fruits = 50+30
Total number of fruits = 80
Percentage of oranges in the basket = Number of oranges in the basket*100/total number of fruits in the basket
Percentage = (30*100)/80
Percentage = 37.5%
Hence, the percentage of oranges is the basket of fruits is 37.5%.
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I am needing help. I do not understand these types of problems.
For angle 45 degree, hypotenuse side is 15 and base side is x.
Determine the measure of side x by using trigonometry.
[tex]\begin{gathered} \cos 45=\frac{x}{15} \\ 0.707=\frac{x}{15} \\ x=15\cdot0.707 \\ =10.605 \end{gathered}[/tex]Thus value of x is 10.605 m.
Answer: x = 10.605 m
e inverse operations to solve the equations below. x^2+3=19
We have the expression:
[tex]x^2+3=19\Rightarrow x^2=16[/tex][tex]\Rightarrow x=\pm4[/tex]Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.(2x - 20)INNISmaller angle:Larger angle:O0UNSFANA(4x - 10)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define complementary angles
When the sum of two angles is 90°, then the angles are known as complementary angles.
STEP 2: Write the pairs of the angles formed
[tex]\begin{gathered} (2x-20)\degree \\ (4x-10)\degree \end{gathered}[/tex]STEP 3: find the value of x
Following the definition in step 1, this goes that;
[tex]\begin{gathered} (2x-20)+(4x-10)=90\degree \\ 2x-20+4x-10=90\degree \\ 6x-30=90 \\ 6x=90+30 \\ 6x=120 \\ x=\frac{120}{6}=20 \end{gathered}[/tex]STEP 4: Find the two pair of angles
[tex]\begin{gathered} (2x-20)=2(20)-20=40-20=20\degree \\ 4x-10=4(20)-10=80-10=70\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} smaller\text{ }angle=20\degree \\ Larger\text{ }angle=70\degree \end{gathered}[/tex]the paper didnt explain how to do this clearly could you take me step by step how to do this
Given data:
The given point is (2,-2).
The equation of the line is y= -2x+3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the given equation with the above equation.
[tex]m=-2[/tex]Two parallel lines have equal slope, the equation of the line parallel to the given line and passing through (2, -2) is,
[tex]\begin{gathered} y-(-2)=m(x-2) \\ y+2=-2(x-2) \\ y+2=-2x+4 \\ y=-2x+2 \end{gathered}[/tex]Thus, the equation of the line is y= -2x+2.
A painter charges $20 for every hour that he paints. Let h equal the number of hours he paints and e represent his earnings.Select TWO equations that represent the situation.A. e= 20hB. h=20+eC. 20=h+eD. 20=hxeE. e/h=20
The form of the linear equation is
[tex]y=mx+b[/tex]m is the rate of change
b is the initial amount
Since The painter charges $20 every hour, then
The rate is 20
m = 20
Since there is no initial amount of payment, then
b = 0
Since the number of hours is h, then
x = h
Since the earning is e, then
y = e
The equation is
[tex]e=20h[/tex]Then the first equation is A
Divide both sides by h
[tex]\begin{gathered} \frac{e}{h}=\frac{20h}{h} \\ \frac{e}{h}=20 \end{gathered}[/tex]The 2nd equation is E
Delta Airlines' flights from Chicago to Atlanta are on time 80 % of the time. Suppose 14 flights are randomly selected, and the number on-time flights is recorded.1.The probability that at least 9 flights are on time is =2.The probability that at most 2 flights are on time is =3.The probability that exactly 10 flights are on time is =
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Given that 14 flights are randomly selected from the record list and that the flights from Chicago to Atlanta are on time 80% of the time, we have to determine:
a) The probability that at least 9 flights are on time
If we choose a flight randomly out of the 14 and 80% of the time it is on time (success), then we can use the binomial theorem for probability:
[tex]\binom{n}{x}p^x(1-p)^{n-x}[/tex]Where p is the probability of success and x is the number of times we want to check.
In this case, let p = 80% or 0.8, n = 14, such that
[tex]\binom{14}{x}0.8^x\cdot0.2^{14-x}[/tex]To find the probability that at least 9 flights are on time, we calculate the probability that at least 5 are not on time. That is, we make
[tex]\begin{gathered} 14-x=5 \\ x=9 \end{gathered}[/tex]Thus
[tex]\binom{14}{9}0.8^9\cdot0.2^5=\frac{14!}{9!\cdot(14-9)!}\cdot0.8^9\cdot0.2^5\approx0.086[/tex]In fact, we have to sum all of the contributions as follows:
[tex]\sum ^{14}_{x=9}\binom{14}{x}0.8^x\cdot0.2^{14-x}[/tex]And we get:
[tex]\approx0.956[/tex]In other words, the probability that at least 9 flights are on time is 95.6%
b) The probability that at most 2 flights are on time
For this, we need to find the probability that at least 13 flights are not on time, such that
[tex]undefined[/tex]How high is the top of the ladder from the ground?
We will use the Pythagorean theorem in order to find the missing value that is the height of the top ladder from the ground
[tex]c^2=a^2+b^2[/tex]In our case
c=10
a=5
b=?
We isolate the b
[tex]b=\sqrt[]{c^2-a^2}[/tex]We substitute the values
[tex]b=\sqrt[]{10^2-5^2}[/tex][tex]b=5\sqrt[]{3}[/tex][tex]b=8.66\approx8.7[/tex]round to the nearest tenth the answer is 8.7 ft
If h is the function given by h(x) = (f • g)(x) where f(x) = squareroot of x and g(x) =(sqrtx)^3, then h(x) =
Given;
[tex]\begin{gathered} f(x)=\sqrt[]{x} \\ g(x)=(\sqrt[]{x)}^3=x^{\frac{3}{2}} \\ (f\circ g)(x)=\sqrt[]{x^{\frac{3}{2}}} \\ h(x)=(f\circ g)(x)=x^{\frac{3}{4}} \end{gathered}[/tex]CORRECT OPTION: D
Given triangle ABC below, if angle B=(x-60)^ and angle C=(x- 45)^ find the measure of angle x
Given:
m∠B = (x - 60)°
m∠C = (x - 45)°
Opposite angle = x°
Let's find the measure of angle x.
To find the measure of angle x, apply the Exterior Angle Theorem which states that the exterior angle of a triangle is equal to the sum of the two opposite angles.
Thus, we have:
∠B + ∠C = x
(x - 60) + (x - 45) = x
Solve for x.
• Remove the parentheses and combine like terms:
x - 60 + x - 45 = x
x + x - 60 - 45 = x
2x - 105 = x
• Move all terms containing x to the left, then move 105 to the right
2x - x = 105
x = 105°
Therefore, the measure of angle x is 105°
ANSWER:
x = 105°
based on the graph which equation can be used to describe the relationship between x and y?
hello
to solve this problem, we can easily find the slope of the line
this will give us the an insight to the answer
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]now let's identify our points
[tex]\begin{gathered} y_2=2 \\ y_1=-4.5 \\ x_2=-13.5 \\ x_1=6 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2--4.5}{-13.5-6} \\ m=\frac{6.5}{-19.5} \\ m=-\frac{1}{3} \end{gathered}[/tex]the slope of the line is -1/3 and this corresponds to option B
the equation of the line is given as
[tex]y=-\frac{1}{3}x-2.5[/tex]