Answer:
Step-by-step explanation:
This problem is solved using the Pythagorean theorem (a2+b2=c2). In this formula a and b are the legs of the right triangle while c is the hypotenuse.
Using the labels of our triangle we have:
o2+a2=h2
\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}
h2=100ft2+289ft2
h=389ft2−−−−−√
So with this information you can see that the correct answer is 19.7ft
What transformation occurs from the graph y = x² to the graph of y = (x − 5)² + 7?
A a vertical shift up 5 units and a horizontal shift right 7.
B a vertical shift down 5 units and a horizontal shift right 7
C a vertical shift up 7 units and a horizontal shift left 5
D a vertical shift up 7 units and a horizontal shift right 5
The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
What do we mean by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.So, the transformation from:
y = x² to y = (x - 5)First, plot both graphs.
(Refer to the graph attached below)
Now, notice that the graph of the function y = (x - 5)² + 7 has shifted vertically upwards by 7 units and horizontally right by 5 units.Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
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if a factory can make 600 nails every 3 minutes, how long would it take to make 27,000 nails?
Answer:
2 hours 15 minutesStep-by-step explanation:
Conditions Given:A factory makes 600 nailsFor making 600 nails the factory takes 3 minutesTo Find:Time taken by the factory to make 27000 nailsSolution:Given,
No. of nails the factory makes = 600
Time taken by the factory to make 600 nails = 3 minutes
So,
Time taken by the factory to make 1 nail = [tex]\frac{3}{600}[/tex] minutes
∴ Time taken by the factory to make 27000 nails
= ( [tex]\frac{3}{600}[/tex] × [tex]27000[/tex] ) minutes
[On simplifying]= ( [tex]\frac{1}{2}[/tex] × [tex]270[/tex] ) minutes
[On further simplifying]= 135 minutes
Or,
As we know , [ 1 minute = [tex]\frac{1}{60}[/tex] hour]
So, 135 minutes = [tex]\frac{135}{60}[/tex] hours
[On simplification]= 2.25 hours
Now, [1 hour = 60 minutes]
0.25 hours = [tex]\frac{1}{4}[/tex] hours
= [tex]\frac{1}{4}[/tex] × 60 minutes
= 15 minutes
Hence,
The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)
Answer:
2.25 hours or 2 hours 15 minutes
Step-by-step explanation:
600 nails / 3 minutes = 200 nails / minute
27,000 nails / 200 nails/minute = 135 minutes
1 hour = 60 minutes
135 minutes × 1 hour / 60 minutes = 2.25 hours
2.25 hours = 2 hours + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes
Answer: 2.25 hours or 2 hours 15 minutes
What is an equation of the line that passes through the point (2,-2)and is perpendicular to the line 5x-2y=4
Answer:
y=-0.4x - 1.2
the probability of serena serving an ace n tennis is 0.15, and the probability that she double faults is 0.25. what is the probability that serena does not serve an ace or a double fault?
The probability that Serena does not serve an ace or a double fault is 0.63..
Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .
We have following information,
The probability of Serena serving an ace in tennis (p) = 0.15
Probability that she double faults(q) = 0.25
The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85
let A and B be two events Serena not serving an ace and she double faults respectively.
Events A and B are not mutually exclusive events .
i.e, P(A ∩ B ) =/ 0
when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.
So, the probability of intersection of event A and B = 0.85/2 = 0.47
Adding Rule for probabilities is
P(A or B ) = P(A) + P(B) - P(A ∩ B)
The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47
= 1.10 - 0.47 = 0.63...
Hence, the probability that Serena does not serve an ace or double fault is 0.63..
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4 tins of soup have a total weight of 1120 grams
3 tins of soup and 5 packets of soup have a total weight of 1015 grams
work out the total weight of 5 tins of soup and 2 packets of soup
on a particular stretch of highway, the state police know that the average speed is 62 mph with a standard deviation of 5 mph. on a busy holiday weekend, the police are concerned that people travel too fast. so they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. let's assume, for the moment, that people travel at the same speed on holiday weekends as they typically do on other days. calculate the mean and standard deviation of the sampling distribution of sample means for samples of size n
The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
What is a standard deviation?
Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Here, we have
µ = 62 , σ = 5
P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / (σ/√(n)
Z = ( 66 - 62 ) / ( 5 / √50 )
Z = 5.6569
P ( ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )
P ( X < 66 ) = P ( Z < 5.66 )
P ( X < 66 ) = 1
P ( X > 66 ) = 1 - P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / ( σ / √(n))
Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )
Z = 5.6569
P ( ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )
P ( Z > 5.66 )
P ( X > 66 ) = 1 - P ( Z < 5.66 )
P ( X> 66 ) = 1 - 1
P ( X> 66 ) = 0
Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
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Which equation represents a line which is perpendicular to the line y=-4x-5?
A.x+4y=−32
B.4x+y=3
C.4x−y=−4
D.4y−x=4
you need to construct a fence around an area of 1600ft2 . what are the dimensions of the rectangular pen to minimize the amount of material needed?
The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.
What is the meaning of minimum dimension?The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.
With regard to the above problem,
let us say L is the lenght of the rectangle and W is the width
Based on the formula for the area of a rectangle,
L x W = 1600ft
To minimize the perimeter, of the rectangle, we must assume that:
L = W
that is L² = 1600
If we applied square root to both sides of the equation, we'd have
L = 40
Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.
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A triangle has sides with lengths of 10 yards, 12 yards, and 14 yards. Is it a right triangle?
yes or no?
Answer:
No
Step-by-step explanation:
The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].
The square of the length of the largest side is [tex]14^2=196[/tex].
Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.
The president of the Huerta Middle School science club suggested a field trip to the local
aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who
goes.
Write an equation showing how the total cost, y, depends on the number of students going,
X.
Do not include dollar signs in the equation.
►
y =
The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x
Equation:
An equation is made up of two expressions connected by an equal sign.
For example, y = 3x + 6 is an equation.
Given,
The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.
Here we need to find the equation that shows the total cost depends on the number of students.
Let us consider x be the number of students and y be the cost for x number of students.
Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.
So, based on these details, the equation for the total cost is calculated as,
=> y = 21.25 + 14.75x
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in right angles , side of all angles. how am I supposed to know what is adjacent to angle I'm trying to find and what is opposite from it.
I know the hypotenuse because it is the biggest one
let k and n be non-negative integers and n be the maximum of the two. what is a k-permutation of n distinct objects? g
If k and n are non-negative integers and n is the greater of the two, then the ordered list of k of the n things without repetition is the k-permutation of the n separate objects.
The total number of ways to select k objects from a set of n elements is n(n1), with (nk+1) alternatives being available for the kth place.when ordering matters and repetition is not permitted. A k-permutation of the elements in set A is any of the chosen lists in the previous configuration (choose k elements, in any order, with no repetition). Pnk=0 if k is greater than n. This makes sense because it is impossible to select k unique elements from an n-element collection if k>n.
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Help me please i really dont understand this question
The measure of θ from the given trigonometric equation is 31°.
Given that, sin47°=cosθ and sinθ=cos(θ+16).
What are complementary angles of trigonometric ratio?We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.
The complementary angles are:
sinθ=cos(90-θ)
secθ=cosec(90-θ)
tanθ=cot(90-θ)
A) So, sin47°=cos(90°-47°)
⇒ sin47°=cos43°
Thus, θ=43°
B) sinθ=cos(θ+16)
⇒ sinθ=cos(43+16)
⇒ sinθ=cos 59°
⇒ sin(90-31)=cos 59°
Thus, θ=31°
Therefore, the measure of θ from the given trigonometric equation is 31°.
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6 x 7/8
(six x seven eighth's) This is a review for last year but I forgot how to do it also can you show how you got it please?
Answer:
5 1/4 // 5.25
Step-by-step explanation:
convert 6 into a fraction:6/1 x 7/8multiply numerators by numerators, and denominators by denominators42/8 (6 x 7 = 42, 8 x 1 = 8)Simplify the fraction using the Lowest Common Multiples42/8 --> 21/4 convert the improper fraction into a mixed number:5 1/4OR
5.25Answer:
5 1/4
Step-by-step explanation:
You want the product of 6 and 7/8.
Product with a fractionYour written-out version of the question gives you a clue how to solve it:
six times seven eighths
The associative property of multiplication lets you rearrange this to ...
(six times seven) eighths = forty-two eighths
That is, the product is formed by multiplying the integer by the numerator, and expressing the whole thing over the denominator:
[tex]6\times\dfrac{7}{8}= \dfrac{6\times7}{8}=\dfrac{42}{8}\\\\=\dfrac{40+2}{8}=\dfrac{40}{8}+\dfrac{2}{8}=5+\dfrac{1}{4}\\\\=\boxed{5\dfrac{1}{4}}[/tex]
Improper fractionThe improper fraction is converted to a mixed number by looking at the quotient and remainder from the division: 42/8 = 5 r 2 = 5 2/8 = 5 1/4.
__
Alternate solution
Sometimes, it can be helpful to look at the problem another way.
6 × 7/8 = 6 × (1 -1/8) = 6 -6/8
= 6 -3/4 = 5 1/4
The normal price of a train ticket from Ashford to London is £34.20
Ross gets 1/3
off the price of his train ticket
Work out how much Ross pays for his ticket.
guys please help lol
Answer:
£22.80
Step-by-step explanation:
To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.
what is 15.0782 rounded to
the nearest 10
Reason:
The digit in the tens place is 1. Just to the right is 5, which tells us to bump the 15 up to 20.
We can say that 15.0872 is closer to 20, than it is to 10.
Be sure not to mix up "tens place" with "tenths place".
The round-off from the number 15.0782 to the nearest 10 will be 20.
What is rounding off to the number?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
Given that the number is 15.0782. The round-off to the nearest 10 will be 20 for the number.
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Can anyone write the equation of the graph?
The absolute value function graphed in this problem is given by the rule presented as follows:
y = |x - 3| + 5.
How to obtain the graph of an absolute value function?The first step to obtain the graph of an absolute value function is obtaining the vertex of the function, which is the turning point of the curve in the format of V.
Then, the definition of an absolute value function with vertex (h,k) is defined by the equation presented as follows:
y = |x - h| + k.
For the graphed function, the coordinates of the vertex are given as follows:
(3,5).
The reason for these coordinates are as follows:
h = 3 as the turning point of the graph is at a coordinate of x = 3.k = 5 as the turning point of the graph is at a coordinate of y = 5.Considering the coordinates of the vertex obtained previously on the problem, the absolute value equation graphed is defined by:
y = |x - 3| + 5.
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One angle of an isosceles triangle measures 80°. What measures are possible for the other two angles? Choose all that apply.
80°,20° or 50°,50° are possible for the other two angles.
Given:
One angle of an isosceles triangle measures 80°.
we assumed that the 80° is one of the equal angles, then there is another 80° angle.That makes 160°.
Since a triangle always totals 180°,
180° - 160° = 20°.
if the 80° was the only different angle instead,the two remaining angles total:
180 - 80 = 100
Since we have two identical angles remaining, we need only divide the 100° in half to get the final answer:
100/2 = 50°.
Therefore 80°,20° or 50°,50° are possible for the other two angles.
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a package of 4 erasers costs $0.39. At this rate, how much would 54 erasers cost, in dollars and cents?
Answer:
Step-by-step explanation:
5 dollars and 25 cents
Consider the equation 2x^(2)+2y^(2)+2x-2y-7-0 Write the equation in the standard form of a circle? What is the center and the radius
help meeeeeeeeeeeeeee pleaseee
The following are features of the parabola shown in the diagram:
Vertex: (2, -1)
Axis of symmetry: x = 2
The parabola opens downward.
What is the Vertex of a Parabola?The vertex of a graph is the coordinates of the point where the tip of the parabola lies at.
What is the Axis of Symmetry of a Parabola?
The axis of symmetry of a parabola passes through the vertex and is it expressed as the x-coordinate of the vertex of the parabola.
The tip of the parabola shown in the image above is at (2, -1), and the parabola as can be seen opens downward.
Therefore:
The vertex of the parabola is (2, -1)
The axis of symmetry would be expressed as x = 2. The parabola opens downward as well.
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giving Brainly show work
Answer:
Step-by-step explanation:
5 1/2 +2x = 25
25- 5 1/2 = 2x
19 1/2 = 2x
x = 9.75
It took him about 9.75 weeks to lose at least 25 pounds.
Answer:
10 or more weeks------------------
Weight lossFirst week - lost 5 and 1/2 pounds,Following weeks - lost 2 pounds per week,Total - at least 25 pounds.Set inequality and find the least whole number2w + 5.5 ≥ 252w ≥ 25 - 2.52w ≥ 19.5w ≥ 19.5/2w ≥ 9.75 ≈ 10It took Mr. Henry at least 10 weeks to lose 25 pounds.
a percentage distribution is given below for the size of families in one u.s. city. size percentage 2 42.8 3 21.1 4 19.2 5 11.6 6 3.3 7 2.0 a family is selected at random. find the probability that the size of the family is 4 or more. round your result to three decimal places.
The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.
Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.
P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)
P(X ≥ 4) = 19.2 + 11.6 + 3.3 + 2.0
P(X ≥ 4) = 36.1
Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.
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(sec(t)-cos(t))/sin(t)
The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)
How to simplify trigonometric ratios?There are different trigonometric ratios such as;
sin x
tan x
cos x
sec x
cosec x
cot x
Now, we want to simplify the trigonometric expression;
(sec(t) - cos(t))/sin(t)
We know that;
sec (t) can be written as 1/cos t
Thus;
(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t
= (1/(sint cos t) - cos t/ sin t
= (1 - cos²t)/(sin t cos t)
= sin²t/(sin t cos t)
= sin t/cos t
= tan t
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which of the following is a reason why a researcher might choose to conduct a double-blind placebo control group study? a. to control for regression to the mean b. to control for observer bias c. to eliminate testing effects d. to prevent attrition
A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.
A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.
This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.
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Select the two values of x that are roots of this equation. x2 + 3x – 5 = 0
The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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jacob has a jar of nickels and dimes. he has twice as many nickels as dimes. he has 310. how many of each type of coin does he have
No. of coins in jar of nickels is 207 and of dimes is 103.
Let the no. of coins of dimes = x
No. of coins of nickels = 2x
Total = 310
x + 2x = 310
3x = 310
x = 310/3
= 103.33
≈ 103
No. of coins of dimes = 103
No. of coins of nickels = 310 - 103
= 207
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5. Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your
reasoning.
Answer:
Andre is taller than Diego
Step-by-step explanation:
There are 100 cm in a meter. If we use this information and convert Diego's height to meters, we find that Diego is 1.65 m. This is a smaller number, and therefore, Diego is shorter than Andre.
The Coast Guard cutter Angelica travels at 30 knots from its home port of Corpus Christi on a course of 95 degrees for 2 hrs and then changes to a course of 185 degrees for 2 hrs. Find the distance and the bearing from the Corpus Christi port to the boat.
The distance and bearing of the boat from the port areas follows;
The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.
What is a bearing in mathematics?A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.
The speed at which the Coast Guard cutter travels = 30 knots
Bearing of the Coast Guard cutter Angelica = 95°
The time the coast guard travels in the initial direction = 2 hours
The direction the Coast Guard cutter changes to = 185°
Time of traveling in the new direction = 2 hours
30 knots = 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km
The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km
From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle
The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15
The distance f the boat from the port is approximately 157.15 kilometers
The base angles of an isosceles right triangle are 45°
Therefore, the bearing is 95° + 45° = 150°
The bearing from the port to the boat is 150°
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Find the values of x and y.
Question content area bottom
Part 1
x
41 (Do not include the degree symbol in your answer.)
Part 2
y
enter your response here (Do not include the degree symbol in your answer.)
Step-by-step explanation:
when a line intersects parallel lines, then the intersecting angles must be the same for each of the parallel lines.
so,
y = 139
and the angles y and x are supplementary (or a linear pair). that means together they have 180°.
that is simply because the sum of all angles around a single point on one side of a line must be 180° (because the line is like the diameter of a circle with the "rotation point" being the center, and one side of the line represents the half-circle).
therefore,
y + x = 180
139 + x = 180
x = 41