Answer:
7.8×10^4
Step-by-step explanation:
move the decmial right til you have a number that is greater than one and less than 10.
count how many you put to the right and put ×10^etc
but it would be opposite if you were trying to reverse it
imani got a notice from the bank saying that she had overspent, so her account balance was -$43. She wrote an additional check for $50 after she overdrew her account. What will be imanis bank account balance once the new check goes through?
Answer:
-93
..................................................................................................................................................
Answer:
i believe its 7 because -43+50 = 7
Step-by-step explanation:
Which ensation is equivalent to square root to x+ 11 = 15?
Answer:
2
Step-by-step explanation:
x + 11 = 15
x = 15 - 11
x = 4
square root of 4 = 2
proof: 2 × 2 = 4
The given table of values represents a linear equation. What is the slope?
Answer:
2
Step-by-step explanation:
slope=∆y/∆x
thus values of y and x at any point in the table can be used.
slope= (7-5)÷(2-1)
slope=2.
identify f(1) and (f2)
Answer:The vowels in the left column are called "front vowels." Tongue body is in the front of the mouth. All vowels show a "gap" in frequency between F1 and F2. ... A traditional "vowel diagram" can be obtained by plotting the vowel formants in a graph where the horizontal axis is (F2-F1) and the vertical axis is inverse F1.
Step-by-step explanation:
Find the Circumference of a circle with a radius of 5
inches. Round your answer to the nearest ten-thousandths.
Please help :(
Answer:
31.42
Step-by-step explanation:
you will need a calculator for this
you will need to do 2 x pi x r = C
2 x 3.14 x 5
2x5=10
3.14 x 10 = 31.42
you get 2 when you round to the nearest ten-thousandths
pi = 3.14159
Answer:
31.4159 inStep-by-step explanation:
Formula for circumference
C = 2πr, where r is radiusSolving for the circle with radius of 5 in
C = 2*π*5 = 10π = 31.4159265359 ≈ 31.4159 in roundedQUESTION 5 Let u = (1, 2, -1), v = (6, 4, 2) € R³. 5.1 Write w = (-3,2,-5) as a linear combination of u and u. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is
1. The vector w = (-3, 2, -5) can be written as a linear combination of u and v.
2. The set {u, v} is linearly independent.
3. The vector w is not in the span of the set {u, v}.
1. To write w as a linear combination of u and v, we need to find scalars a and b such that w = au + bv. By solving the system of equations, we get:
-3 = a1 + b6,
2 = a2 + b4,
-5 = a*(-1) + b2.
Solving these equations, we find a = 2 and b = -1. Therefore, w = 2u - v.
2. The set {u, v} is linearly independent if the only solution to the equation au + bv = 0 is a = b = 0. We can write this equation as a system of equations:
a + 6b = 0,
2a + 4b = 0,
-a + 2b = 0.
Solving this system, we find that the only solution is a = b = 0. Therefore, the set {u, v} is linearly independent.
3. To determine if the vector w is in the span of {u, v}, we need to check if there exist scalars a and b such that w = au + bv. However, from the previous calculation, we found that w can be expressed as a linear combination of u and v with a = 2 and b = -1. Therefore, w is not in the span of {u, v}.
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find the measure of angle 1
Answer:
90
Step-by-step explanation:
On a mountain, the temperature decreases by 6.5°C for every 1000 metres increase in height.
At 2000 metres the temperature is 10 °C.
Find the temperature at 6000 metres.
Based on the temperature at 2,000 meters and the rate of temperature change, the temperature at 6,000 meters is -16°C.
The difference between 2,000 meters and 6,000 meters is:
= 6,000 - 2,000
= 4,000 meters
For every 1,000 meters increase, the temperature will drop by 6.5 °C. At 4,000 meters:
= 6.5 x 4,000 / 1,000
= 26 °C
The temperature will reduce by 26°C to become:
= Temperature at 2,000 - Temperature change
= 10 - 26
= -16 °C
In conclusion, the temperature is -16 °C.
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Prove, or disprove by means of a counterexample, each of the following statements. (i) The sum of a finite number of convex subsets of R n is convex. (ii) The collection of all convex subsets of R 2 a linear space. (iii) The sum of two closed subsets of R n is closed. (iv) Does the sentence in (iii) above make sense if (X,d) is substituted for R n ? If so, prove it. If not, justify the claim that it is incoherent. (v) The projection onto any particular coordinate of a closed subset of a metric space R n is closed. [Recall that for any A⊆R n , its projection on to the i th -cordinate, i=1,⋯,n, is denoted by proj i A={y i ∈R:(y 1 ,y 2 ,⋯,y n )∈A}.]
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
Proof: Let A_1, A_2, ..., A_k be convex subsets of R^n. We want to show that the set B = A_1 + A_2 + ... + A_k (which is the set of all possible sums of elements from each A_i) is convex.
Let x, y ∈ B and let α ∈ [0, 1]. Since x and y are in B, there exist vectors a_1, a_2, ..., a_k and b_1, b_2, ..., b_k such that x = a_1 + a_2 + ... + a_k and y = b_1 + b_2 + ... + b_k, where a_i, b_i ∈ A_i for each i = 1 to k.
Now consider the point z = αx + (1 - α)y. We need to show that z is also in B.
z = αx + (1 - α)y
= α(a_1 + a_2 + ... + a_k) + (1 - α)(b_1 + b_2 + ... + b_k)
= (αa_1 + (1 - α)b_1) + (αa_2 + (1 - α)b_2) + ... + (αa_k + (1 - α)b_k)
Since each A_i is convex, we have αa_i + (1 - α)b_i ∈ A_i for all i = 1 to k. Therefore, z belongs to the set B = A_1 + A_2 + ... + A_k.
Hence, the sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
Counterexample: Consider two convex subsets of R^2, A = {(x, y) ∈ R^2 : x > 0} (the right half-plane excluding the y-axis) and B = {(x, y) ∈ R^2 : x < 0} (the left half-plane excluding the y-axis). Both A and B are convex subsets of R^2.
Now, let's consider their sum, A + B. For any point (x, y) in A + B, there exist points (a, b) from A and (c, d) from B such that (x, y) = (a, b) + (c, d). However, (a + c, b + d) must lie on both the right half-plane and the left half-plane simultaneously, which is not possible. Therefore, A + B is not a valid convex subset of R^2.
Hence, the collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
Counterexample: Consider the closed subsets A = [0, 1] and B = [2, 3] of R. Both A and B are closed intervals in R.
The sum A + B = [0, 1] + [2, 3] = [2, 4]. However, [2, 4] is not closed since it does not contain its limit points, specifically the point 3.
Therefore, the sum of two closed subsets of R^n is not always closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
The concept of "closed" subsets relies on the notion of limits and convergence, which is defined in the context of metric spaces. If (X, d) is a general metric space, the idea of closed subsets and their properties may vary depending on the specific metric and topology of the space. Therefore, it is not meaningful to discuss the closure of subsets in a general metric space without further specifying the properties of that particular space.
Hence, the claim is incoherent unless additional information about the specific metric space (X, d) is provided.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
Proof: Let A be a closed subset of R^n, and consider its projection onto the i-th coordinate, proj_i(A) = {y_i ∈ R : (y_1, y_2, ..., y_n) ∈ A}.
We need to show that proj_i(A) is closed. To do this, we can show that its complement, proj_i(A)^c, is open.
Let x ∈ proj_i(A)^c. This means that x is not in proj_i(A), so there exists some (a_
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solve the equation: 7+x/5=18
Answer:
x = 83
Step-by-step explanation:
Which of these numbers is the largest?
47 896
48 769
74 968
86974
87946
Answer:
last one
Step-by-step explanation:
A restaurant sold 350 less hotdogs than hamburgers. Altogether, the restaurant sold 700 hotdogs and hamburgers. How many of each did they sell?
Answer:
hey hotty
Step-by-step explanation:
Use the properties of the natural logarithm to expand each logarithmic expression. Round answers to 3
decimal places, if necessary. a. In(7x) = Preview 5x b. In Preview x + 3 c. In (x 8) = Preview d. 15,000 In(xy4) =
a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).
a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).
Therefore, ln(7x) can be expanded as ln(7) + ln(x).
b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).
Hence, ln(x + 3) remains as it is since we cannot simplify it further.
c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).
Thus, ln(x^8) becomes 8 * ln(x).
d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).
Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].
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Given the function f (x) = x2 – 52, find f (x - 3) f (x – 3)
an engineering research center claims that through the use of a new computer control system, automobiles should achieve, on average, an additional 3 miles per gallon of gas. a random sample of 100 automobiles was used to evaluate this product. the sample mean increase in miles per gallon achieved was 2.4, and the sample standard deviation was 1.8 miles per gallon. test the hypothesis that the population mean is at least 3 miles per gallon. find the p-value of this test, and interpret your findings
The results suggest that the new computer control system has a statistically significant impact on improving fuel efficiency, with the average increase in miles per gallon being less than 3.
How to calculate the valueLet's calculate the t-score:
t = (2.4 - 3) / (1.8 / √100)
t = -0.6 / (1.8 / 10)
t = -0.6 / 0.18
t ≈ -3.33
Since we're testing the hypothesis that the population mean is at least 3 (greater than 3), we're performing a one-tailed test. We need to find the p-value for the t-score of -3.33 in the right tail of the t-distribution.
The p-value can be found using statistical software or a t-table. Assuming an alpha level (significance level) of 0.05, the p-value is less than 0.001 (highly unlikely to occur by chance). This indicates strong evidence against the null hypothesis.
Since the p-value is less than the significance level (α = 0.05), we reject the null hypothesis. The results suggest that the new computer control system has a statistically significant impact on improving fuel efficiency, with the average increase in miles per gallon being less than 3.
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Select the correct answer.
A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of
. What is the approximate distance from the playground to the road along the other path?
The picture shows an upside-down right-angle triangle. The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 mi and the swing stands on the downside of the triangle
A.
2.6 mi
B.
1.5 mi
C.
3.1 mi
D.
1.3 mi
The approximate distance from the playground to the road along the other path is 1.3 miles.
How to find the side of a right triangle?The angle of the top vertex is 50 degrees. The length of the hypotenuse is 2 miles and the swing stands on the downside of the triangle.
Using trigonometric ratios, let's find the approximate distance from the playground to the road along the other path as follows:
cos 50 = adjacent / hypotenuse
cos 50° = x / 2
cross multiply
x = 2 cos 50°
x = 2 × 0.64278760968
x = 1.28557521937
x = 1.3 miles
Therefore,
distance from the playground to the road along the other path = 1.3 miles
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XY bisects RS at point M. If RM = 6, find the length of RS.
Answer: RS = 6
Step-by-step explanation: Not 100% sure but that's what I think the answer is.
A geometry class is asked to find the equation of a line that is parallel to y – 3 = −(x + 1) and passes through (4, 2). Trish states that the parallel line is y – 2 = –1(x – 4). Demetri states that the parallel line is y = –x + 6.
Are the students correct? Explain.
Trish is the only student who is correct; the slope should be –1, and the line passes through (4, 2).
Demetri is the only student who is correct; the slope should be –1, and the y-intercept is 6.
Both students are correct; the slope should be –1, passing through (4, 2) with a y-intercept of 6.
Neither student is correct; the slope of the parallel line should be 1.
Answer:
C
Step-by-step explanation:
Both students are correct; the slope should be –1, passing through (4, 2) with a y-intercept of 6.
Answer: Its c
Step-by-step explanation:
Both students are correct.
3 t-shirts and 2 hats costs £14.
2 t-shirts and 7 hats costs £15.
Find the cost of a t-shirt.
Find the cost of a hat.
t-shirt: £
o
hat: £
PLZ HELP
Two sides of a four-sided figure have negative slopes. Which are the endpoints of the sides of this figure?
1. (–4, –4), (–4, –1), (–1, –4), (–1, –1)
2. (–2, –4), (–1, –1), (1, –1), (2, –4)
3. (1, 1), (2, 4), (5, 4), (4, 1)
4. (1, 4), (2, 1), (5, 1), (4, 4)
Answer:
its a
Step-by-step explanation:
Answer:
The answer is 2
Step-by-step explanation:
The reason I chose this answer is because if you have a four-sided figure and 2 sides are negative then you come up with this answer.
3/4 < 4/9 *
1 point
True
False
Answer:
false
Step-by-step explanation:
4/9 is smaller than 3/4.
7. If g(x) = -6x + 5 and h(x) = -9x - 11, find (goh)(x).
you are required to push a 180 pound ball to a storage platform 15 feet higher than where you are now. you can use a 45 foot long ramp to push the ball up. how much effort is required to push the ball up the platform using the ramp?
60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.
To determine the effort required to push the 180-pound ball up a 15-foot high platform using a 45-foot long ramp, we need to consider the forces involved and apply the principles of work and energy.
The work done to raise the ball to the platform is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force applied is the effort required to push the ball up the ramp, and the distance is the length of the ramp.
First, we need to calculate the mechanical advantage of the ramp. The mechanical advantage is the ratio of the length of the ramp to the vertical height it lifts the object. In this case, the mechanical advantage is 45/15 = 3.
Next, we calculate the weight of the ball, which is 180 pounds.
The effort required can be determined using the formula:
Effort = (Weight of the ball) / (Mechanical advantage)
Effort = 180 pounds / 3 = 60 pounds
Therefore, approximately 60 pounds of effort is required to push the 180-pound ball up the 15-foot high platform using the 45-foot long ramp.
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what is the base of a triangle if the height is 6mm and the area is 36
Answer:
b=1.2×107mm
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Five less than twice a number is greater than 13. Then solve.
Answer: The answer should be -4
Step-by-step explanation:
The auto repair on First Street charges a flat fee of $15 plus $10 an hour for servicing a car. The auto repair shop on Second Avenue charges no flat fee but $15 an hour for servicing a car. Malik finds that when he gets his car serviced at either shop, he pays the same amount of money. How many hours does Malik's car need to be serviced?
Answer:
3 hours
Step-by-step explanation:
Let's express number of hours required for servicing as: x
The auto repair on First Street charges a flat fee of $15 plus $10 an hour for servicing a car.
This is expressed mathematically as:
$15 + $10 × x
= 15 + 10x
The auto repair shop on Second Avenue charges no flat fee but $15 an hour for servicing a car
This is expressed as:
$15 × x
= 15x
The number of hours Malik's car needs to be serviced in order to be able to pay the same amount of money at both shops is calculated as:
Charges by Auto repair shop on First street = Charges by Auto repair shop on Second Avenue
15 + 10x = 15x
15 = 15x - 10x
15 = 5x
5x = 15
x = 15/5
x = 3 hours
Therefore, the number of hours Malik's car needs to be serviced in order to be able to pay the same amount of money at either auto repair shops is 3 hours
Write an equation in point-slope form of the line that passes through the point (4,7) and has a slope of -1.
Answer:
y - 7 = - 1(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 1 and (a, b) = (4, 7) , thus
y - 7 = - (x - 4)
The equation of line in the point-slope form is y = -1x + 11
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the point be P = P ( 4 , 7 )
Let the slope of the line be m = -1
So , the equation of line is given by the formula
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 7 = -1 ( x - 4 )
On simplifying the equation , we get
y - 7 = -1x + 4
Adding 7 on both sides of the equation , we get
y = -1x + 11
y = -x + 11
Therefore , the value of A is y = -x + 11
Hence , the equation of line is y = -x + 11
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A geometric sequence has a first term of 3 and a fourth term of 81÷8.
Find the eighth term
Answer:
6561 / 128
Step-by-step explanation:
The nth term of a geometric sequence is:
a = a₁ (r)ⁿ⁻¹
The first term is 3, and the fourth term is 81/8.
81/8 = 3 (r)⁴⁻¹
27/8 = r³
r = 3/2
The eighth term is therefore:
a = 3 (3/2)⁸⁻¹
a = 6561 / 128
what is the formula in finding 5th term in sequence 1,3,7,15,
Answer:
ans is 31
Step-by-step explanation:
the formula in finding 5th term in sequence is 31
Answer:
2n + 1
Step-by-step explanation:
2n + 1 it goes like this
1×2 + 1 = 3
2×3 + 1 = 7
2×7 + 1 = 15
2 × 15 + 1 = 31
A scuba diver dove from the surface of the ocean to an elevation of -79 9/10 feet at a rate of -21.3 per minute. After spending 10.5 minutes at that elevation, the diver ascended to an elevation of -8 9/10 feet. The total time for the dive so far was 17 1/8 minutes. What was the rate of change in the diver's elevation ascent? Round you answer to the nearest hundredth.
Answer:
The rate of change of the divers elevation is approximately 24.71 feet/minute
Step-by-step explanation:
The given information are;
The depth to which the scuba diver dove =[tex]-79\frac{9}{10} \ feet[/tex]
The rate at which he dove = -21.3 feet/minute
The time which he spent at that elevation = 10.5 minutes
The elevation the diver then ascended to = [tex]-8\frac{9}{10} \ feet[/tex]
The total time for the dive = [tex]17\frac{1}{8} \ minutes[/tex]
Therefore, the time, [tex]t_d[/tex], with which the scuba diver descended to [tex]-79\frac{9}{10} \ feet[/tex] is given as follows;
[tex]t_d = \dfrac{Distance}{Speed} = \dfrac{-79\frac{9}{10} }{-21.3} \approx 3.75 \ minutes[/tex]
The time, [tex]t_e[/tex], it took the scuba diver to elevate to [tex]-8\frac{9}{10} \ feet[/tex] is given as follows;
[tex]t_e[/tex] = [tex]17\frac{1}{8} \ minutes[/tex] - (3.75 + 10.5) minutes ≈ 2.8738 minutes
The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken)
∴ The rate of change of the divers elevation = ([tex]-8\frac{9}{10} \ feet[/tex] - ([tex]-79\frac{9}{10} \ feet[/tex] ))/(2.87 minutes) = 71/2.8738 ≈ 24.71 feet/minute to the nearest hundredth
The rate of change of the divers elevation ≈ 24.71 feet/minute.
