Answer:
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Step-by-step explanation:
Given;
Angle of elevation = 3°
Height of arch = 630 ft
Tanθ = opposite/adjacent
Opposite = 630 ft
Adjacent = d
Substituting the values;
Tan3 = 630/d
d = 630/tan3
d = 12,021.1 ft
The Gateway Arch is 12,021.1 ft away
Answer:
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
Step-by-step explanation:
The distance is given by the following trigonometric equation:
[tex]x = \frac{y}{\tan \alpha}[/tex]
[tex]x = \frac{630\,ft}{\tan 3^{\textdegree}}[/tex]
[tex]x = 12021.1\,ft\,(2.3\,mi)[/tex]
Mike purchased a round wall clock the clocks radius is 10m what is the circumference of the clock
Answer:
62.8 m
Step-by-step explanation:
The circumference of the clock is the circumference of a circle which is given by
2 Pi r
Where
Pi = 3.14
Radius r = 10m
Therefore
Circumference = 2 x 3.14 x 10
= 62.8 m
The circumference of the clock is approximately 62.8 meters.
Explanation:To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the radius of the clock is given as 10m. Substituting this value into the formula, we have C = 2π(10) = 20π. The approximate value of π is 3.14, so the circumference of the clock is approximately 20(3.14) = 62.8m.
To find the circumference (C) of a round wall clock, you can use the formula C = 2πr, where π (pi) is approximately 3.14 and r is the radius of the clock. In this case, the radius is given as 10 meters. Substituting this value into the formula, the circumference is calculated as C = 2 * 3.14 * 10 meters, which equals 62.8 meters.
Therefore, the circumference of Mike's round wall clock is approximately 62.8 meters. This value represents the total distance around the edge or perimeter of the circular clock face.
a coin is flipped and a number cube is rolled what is the sample space for this experiment
Answer:
h1,h2,h3,h4,h5,h6,t1,t2,t3,t4,t5,t6
Step-by-step explanation:
h or t is the coin, the number is the die
Final answer:
The sample space for flipping a coin and rolling a number cube consists of 12 possible outcomes. The probability of event A occurring is 1/6. Events A and B are mutually exclusive as they cannot occur at the same time.
Explanation:
A coin is flipped and a number cube is rolled; the sample space for this experiment can be listed by combining each possible outcome of the coin flip with each possible outcome of the number cube roll. The coin can either be heads (H) or tails (T), and the number cube, which is a six-sided die, can land on any number from 1 to 6.
H1
H2
H3
H4
H5
H6
T1
T2
T3
T4
T5
T6
Therefore, the sample space consists of 12 possible outcomes.
For part b, event A is "either a three or a four is rolled first, followed by landing a head on the coin toss." The favorable outcomes for event A are H3 and H4. Since there are 12 possible outcomes, and 2 of them are favorable, the probability P(A) is 2/12, which simplifies to 1/6.
For part c, event B is "the first and second tosses land on heads," which is not possible since the first "toss" is actually a roll of a die. Therefore, events A and B are mutually exclusive, as they cannot occur simultaneously. The occurrence of event A does not involve a second toss of the coin and event B is not possible within the context of this experiment.
Select the correct answer.
What is the justification for step 3 in the solution process?
10d − 5 = 4d − 15 − 3d
Step 1: 10d − 5 = d − 15
Step 2: 9d − 5 = -15
Step 3: 9d = -10
Answer: subtraction property of equality
Step-by-step explanation:
subtracting d from both sides is the subtraction property of equality
Answer:
subtraction property of equality
Step-by-step explanation:
Based on your results in Question 1, how is the volume of the cone related to the volume of the cylinder, given that their bases and heights are the same? (Keep in mind that the volumes you recorded were rounded, not exact values.)
Answer:
in a similar way,the volume of a cone and a cylinder that have identical bases and height are proportional. if a cone and a cylinder have bases (shown in color) with equal areas and both have identical heights, the the volume of a cone is one-third that volume of a cylinder is V=πr2h
Step-by-step explanation:
Answer:
If the base dimensions and the heights are the same, the volume of the pyramid is approximately 1/3 the volume of the cube.
Step-by-step explanation:
awnser for plato math
Please help me solve this ASAP
Answer:
x = (164 - y)/5
y = 165 - 5x
Step-by-step explanation:
A whole rotation is 360° (All the angles together = 360°)
148 + 2x + 47 + y + 3x = 360
195 + 5x + y = 360
165 = 5x + y
y = 165 - 5x
5x = 165 - y
x = (164 - y)/5
If x varies directly as y and x= 18 when y =3 find x when y=7
Answer:
42
Step-by-step explanation:
x = Ky
18 = K(3)
K = 18/3 = 6
x = 6y
x = 6(7) = 42
Please Help me !! Really I don’t know
A school dedicated 50% of the courtyard area for students to start a garden. The students
want to know how much of the 632-square-foot space they will be able to use.
Which expression shows a way to find 50% of 632?
.632
2
.632
Answer:
A. 50% of 632
Step-by-step explanation:
The percentage refers to the whole garden (632) and the amount of this garden they will be able to use. If you need to find the exact number I suggest turning the percent into a fraction (50% is also 1/2) then multilying it by the total (632).
Answer:
317
Step-by-step explanation:
You can find the answer via the equation
632*50%
or
632/2
can someone pls solve this for me
Given:
m∠WYX = 20°
m∠XYZ = 135°
To find:
The measure of arc WXZ.
Solution:
m∠WYZ = m∠WYX + m∠XYZ
m∠WYZ = 20° + 135°
m∠WYZ = 155°
The measure of inscribed angle is half of the intercepted arc.
[tex]$\Rightarrow m \angle WYZ = \frac{1}{2} m (ar WXZ)[/tex]
[tex]$\Rightarrow 155^\circ = \frac{1}{2} m (ar WXZ)[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times 155^\circ = 2 \times \frac{1}{2} m (ar WXZ)[/tex]
[tex]$\Rightarrow 310^\circ = m (ar WXZ)[/tex]
The measure of arc WXZ IS 310°.
tyrell, katy and lucy were eating grapes. tyrell ate twice as many grape as katy, and lucy ate half as many grapes as katy. if katy ate 6 grapes, how many grapes did the three of them eat in all.
Answer:
21
Step-by-step explanation:
k=6 t=k *2=12 l=k/2 =3 6+12+3=21
Answer:
21
Step-by-step explanation:
To find out how much Tyrell ate, you multiply 6 times two (which is 12), then to find out how much Lucy ate, you have to divide 2 and 6 (Which is 3) . Now you add up how many they ate in all.. 6 (Katy) plus 12 (Tyrell) and that equals 18, then you add 3 (Lucy), which comes to a total of 21
120 students in a fifth grade class are surveyed about what kinds of pets they have. Of the 120 students,
30 have a goldfish, 40 have a mouse, and 10 have a goldfish and a mouse. Using this information, answer
each of the following questions.
Let G be the event that a randomly selected student has a goldfish and M be the event that a randomly
selected student has a mouse.
What is P(G), the probability that a student in the class has a goldfish?
What is P(M), the probability that a student in the class has a mouse?
What is P(G and M), the probability that a student in the class has a goldfish and a mouse?
What is PG or M), the probability that a student in the class has a goldfish or a mouse?
Answer: P(G) = 1/4
P(M) = 1/3
P(G and M) = 1/12
P(G or M) = 1/2
Step-by-step explanation:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total Students Surveyed = 120
30 have a goldfish, 40 have a mouse, and 10 have a goldfish and a mouse.
First, the the probability that a student in the class has a goldfish
P(G) = 30/ 120
= 1/4
second, the probability that a student in the class has a mouse
P(M) = 40/120
= 1/3
Third, the probability that a student in the class has a goldfish and a mouse
P(G and M) = 1/4 x 1/3
= 1/12
Fourth the probability that a student in the class has a goldfish or a mouse
P(G or M) = P(G)+ P(M) - P( G and M)
= 1/3+ 1/4 - 1/12
= 6/12
= 1/2
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I will give you brainliest plz help me
Answer:
There are 36 cubes
Step-by-step explanation:
Answer:
18 cm or 36 cubes
Step-by-step explanation:
hxlxb
h=3
l=3
b=4
3x3x4
36
36 divided by 2 since each cube is half
18
Which pair of ratios form a proportion? 97 points
5 : 10 and 10 : 15
8 : 12 and 18 : 27
9 : 15 and 24 : 30
6 : 20 and 7 : 30
Answer:
8 : 12 and 18 : 27
Step-by-step explanation:
5 : 10 and 10 : 15
Divide each by 5
1:2 and 2:3 The ratios are not the same
8 : 12 and 18 : 27
Divide the first by 4 and the second by 9
2:3 and 2:3 This is a proportion
9 : 15 and 24 : 30
Divide the first by 3 and the second by 6
3:5 and 4:5 The ratios are not the same
6 : 20 and 7 : 30
Divide the first by 2 and leave the second alone
2:10 and 7: 30 The ratios are not the same
Answer:
B. 8 : 12 and 18 : 27
Step-by-step explanation:
8 : 12
Reduces to
2 : 3
18 : 27
Reduces to
2 : 3
Same simplified ratio, hence proportional
Which graph represents the function given by the table of values? A) A B) B C) C D) D
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
f(x)=x^2 what is g(x)
Answer:
Step-by-step explanation:
when x=2,g(x)=1
from B when x=2
g(x)=1/4×2²=1
which is true .
so B
Please help!
How do I tell the difference between sss and sas?
SSS (Side-Side-Side) requires three pairs of equal sides to prove triangle congruence, while SAS (Side-Angle-Side) requires two pairs of equal sides and one pair of equal included angles.
Explanation:In mathematics, specifically in geometry, SSS (Side-Side-Side) and SAS (Side-Angle-Side) are two methods used to determine if two triangles are congruent. Congruent triangles are triangles that have the same size and shape.
SSS (Side-Side-Side)
The SSS criterion states that if all three sides of one triangle are respectively equal in length to all three sides of another triangle, then the two triangles are congruent. You do not need to know any angle measurements.
SAS (Side-Angle-Side)
The SAS criterion states that if two sides and the included angle (the angle between the two sides) of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
To distinguish between the two, remember that for SSS you're comparing three sides, and for SAS you're comparing two sides and the angle that is between them.
A gate is 3 feet tall and casts a shadow 5 feet long. At the same time, a nearby building is 27 ft tall. If this is to be a proportional relationship, what is the length of the building's shadow?
Answer:
the length of the shadow is 45 feet long
Step-by-step explanation:
Part A picture above
Part B. What are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin?
A. D’(0,2)
B. D’(0,5)
C. D’(0,10)
D. D’(10,0)
Answer:
Part A C = (10,5) Part B C. D'(0,10)
Step-by-step explanation:
Part A
Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5
(2,1) * 5 = (10,5)
The new point C is going to be (10,5)
Part B
If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from the origin by 5.
In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)
Choose all of the problems that result in an answer of 8.5.
A) 0.85 × 101
B) 85 × 101
C) 85 ÷ 101
D) 0.85 ÷ 102
E) 0.085 × 102
Answer:E
Step-by-step explanation:
Type it all into a calculator
Express this equation in logarithmic form.
4^0.5=2
Answer:
Log₄2=0.5
Step-by-step explanation:
Answer:
[tex]log_{4}[/tex] 2 = 0.5
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]4^{0.5}[/tex] = 2 ← with x = 2, b= 4 and n = 0.5, then
[tex]log_{4}[/tex] 2 = 0.5
Angles A and B are two acute angles in a triangle. If sin A equals cosine B, what can you conclude about the triangle?
Answer:
It's a right angle triangle with 90° at C
Step-by-step explanation:
sin A = cosB when
A + B = 90
The condition that sin A equals cosine B, with A and B being acute angles, indicates that both angles are complementary and add up to 90 degrees, suggesting a right-angled triangle.
Explanation:When given the condition that sin A equals cosine B in a triangle, and both angles A and B are acute, we can determine that triangle A and B are complementary, which means they add up to 90 degrees.
This is due to the co-function identity, where sin(90° - θ) = cos(θ) and cos(90° - θ) = sin(θ) for acute angles in right-angled triangles.
If A and B are in the same triangle, and given it is a right triangle (since they are acute and the sine of one equals the cosine of the other), we can conclude that A + B = 90°, and thus, the third angle will also be 90 degrees, making the triangle a right-angled one.
Maia mixed a batch of punch for the class party. Her recipe called for 3½ cups of orange juice, 2½ cups lemonade, and 2 quarts of ginger ale. How many 1-cup servings does the recipe make?
Answer:
10
Step-by-step explanation:
3 1/2 cups of orange juice
2 1/2 cups of lemonade
1 quart = 4 cups
4 cups of ginger ale
add them all together...
so there should be:
10 1-cup servings!
i hope this helped you!!
:)
2/5 divided by 4 ..........................................
Step-by-step explanation:
When 2/5 is divided by 4 we get or we can do the reciprocal
Here we Get
2/5 * 1/4
= 1 / 10
Answer:
2/20 = 1/10
Step-by-step explanation:
John surveyed 25 of his classmates about their music preferences7 students said they like hip-hop, 13 students said they pop, and 8 students said they liked neither hip-hop nor pop musicJohn made a Venn diagram to find the number of students who like both hip-hop and pop music Evaluate John's work Did he use the Venn diagram accurately to arrive at a correct solution?
Answer:
The venn diagram is not included in the question, but il try to answer it in a general way.
We have a sample of 25 persons.
7 of them like hiphop.
13 of them like pop
8 of them do not like neither.
So in our Venn diagarm we will have two circles, one for the students that like pop and other for the students that like hip-hop.
in the pop circle we have 13 students, in the circle of hiphop we have 7 students, and outside both circles we have 8 stundents.
Now, if we add it all we get:
13 + 7 + 8 = 28,
But we have 25 students, this means that 3 of the students like both genres, hip hop and pop.
Then the circles of hip hop and pop must have an intersection, and in the intersection we must have 3 students.
Toni is considering a 3/27 balloon mortgage with an interest rate of 5.1% to
purchase a house for $121,000. What will be her balloon payment at the end
of 3 years?
O
A. $109,715.78
O
B. $108,908.33
O
C. $108,983.14
O
D. $115,460.91
Answer:the answer is D
Step-by-step explanation:
$115,460.91
Her balloon payment at the end of 3 years is $115,460.91. The correct option is D.
What is balloon mortgage?A balloon mortgage is one of the loan with low initial payments but the borrower is needed to repay the balance in a lump sump amount.
Given is the 3/27 balloon mortgage with an interest rate of 5.1% to purchase a house for $121,000.
The rate is fixed for a period of 3 years and later converts to a new fixed rate for the left 27 years.
using the formula for balloon payment.
FV = P*(1+r)n–P*[(1+r)n–1/r]
Substitute P = $121000, r = 5.1 and n=3 years, we get the balloon payment is
FV = $115,460.91
Thus, her balloon payment at the end of 3 years is $115,460.91. The correct option is D.
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ABCD shown in the coordinate plane below, is dilated with the center at the origin to form quadrilateral
EFGH
What is the scale factor of the dilation?
tontit
A. 1/4
B. 1/3
C. 3
D. 4
Answer:C
Step-by-step explanation:
When a number is increased by 48%, the result is 92. What is the original number to the nearest tenth?
Answer:
So you are trying to find 48% of 92, correct?
Step-by-step explanation:
Answer:
44.2
Step-by-step explanation:
Take 92 and multiply it by .48
what does m equal in this equation, m-7=17
Answer:
Given
m - 7 = 17
m = 17 +7
Therefore m = 24
Answer:
m=24
Step-by-step explanation:
Since m-7=17
We are to find the value of m
And this can be done by making m the subject of formula
So m-7=17
Add 7 to both sides
m=17+7
m=24
Therefore m is 24
What are two ways that mathematics are present in nature?
Answer:
These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature.
Hope this Helps!
Sincerely; Victoria <3
Which table represents a linear function? Explain how you know.
Answer:
Table A represents a linear function. I know because the rate of change between the x and y values is always 1. If you look at the table diagonally, you can see that you can add one to all of your x values to get your y.
Step-by-step explanation: