After the 2004 Olympic games, the scoring system for gymnastics was overhauled. Rather than rank performances from 0 points to 10 points as the old system did, the new system uses a start value and difficulty value to determine the overall score for a routine.
The start value, which is based on the difficulty of the routine, is used as a base score. Points are then deducted for errors, such as falls, wobbles, and other mistakes, resulting in the final score. Under the new system, scores are no longer limited to a maximum of 10 points.
The system has been well received for its ability to differentiate between athletes and their routines more accurately, and it has led to an increase in the difficulty and creativity of routines.
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\large f\left(x\right)=2\left(x+5\right)^2-7
Which word could you use to describe the author's purpose in an argument?
Convince
Describe
Entertain
Inform
g the opening price of a particular stock is modeled as a continuous random variable that is uniformly distributed on the interval [35 3 4, 44 1 4]. what is the probability that, on any given day, the opening price is less than 40?
The probability that the opening price of the stock is less than 40 is approximately 0.5588 or 55.88%.
The opening price of the stock is modeled as a continuous random variable that is uniformly distributed on the interval [35 3/4, 44 1/4].
The probability that the opening price is less than 40 can be found by calculating the area under the probability density function of the uniform distribution between 35 3/4 and 40.
The probability density function of a uniform distribution on the interval [a, b] is given by:
f(x) = 1/(b-a) for a <= x <= b
f(x) = 0 otherwise
In this case, a = 35 3/4 and b = 44 1/4. Therefore, the probability density function of the opening price is:
f(x) = 1/(44 1/4 - 35 3/4) = 1/8.5 = 0.1176 for 35 3/4 <= x <= 44 1/4
f(x) = 0 otherwise
To find the probability that the opening price is less than 40, we need to integrate the probability density function from 35 3/4 to 40:
P(X < 40) = ∫[35 3/4, 40] f(x) dx = ∫[35 3/4, 40] (1/8.5) dx
= [(1/8.5) * x] from 35 3/4 to 40
= (1/8.5) * (40 - 35 3/4)
= 0.5588
Therefore, the probability that the opening price of the stock is less than 40 is approximately 0.5588 or 55.88%.
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A small pool for children has some water in it. Jabari uses a garden hose to add water to it.
The total amount of water in gallons, y, is a function of the time in minutes since Jabari turns
on the hose, a.
-)
The graph of the linear function passes through the points (2, 44) and (5, 80).
What is the equation of the function?
y= 12 + 20
How much water is in the pool when Jabari turns on the hose?
Answer:
20 gallons.
Step-by-step explanation:
The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the two given points, we get:
m = (80 - 44) / (5 - 2)
m = 12
To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:
y - y1 = m(x - x1)
y - 44 = 12(x - 2)
y - 44 = 12x - 24
y = 12x + 20
So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:
y = 12x + 20
When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:
y = 12(0) + 20
y = 20
Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.
The difference between the monthly high
and low temperatures was less than 27°
Fahrenheit. The monthly low temperature
was
-2° Fahrenheit. Determine the possible
monthly high temperature. Then interpret
the solution.
The possible monthly high temperature is less than 25°.
What is the possible monthly high temperature?It's important to note that temperature simply means the degree of hotness and the coldness that a particular medium has.
In this situation, the difference between the monthly high and low temperatures was less than 27° Fahrenheit and monthly low temperature
was -2° Fahrenheit. Therefore, the monthly high will be:
High - Low < 27
High - (-2) < 27
High + 2 < 27
High < 27 - 2
High < 25
The interpretation means that the temperature is less than 25°F.
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please answer fast ! thanks
A quadratic functiοn f whose zeroes are 2 and 5 is f(x) = x² - 7x + 10.
WHAT IS QUADRATIC FUNCTION?A quadratic functiοn is a secοnd-degree pοlynοmial functiοn οf the fοrm:
f(x) = ax² + bx + c
where a, b, and c are cοnstants, and a is nοt equal tο 0. The graph οf a quadratic functiοn is a parabοla, which can οpen upwards οr dοwnwards depending οn the sign οf the leading cοefficient a.
The term ax² is the quadratic term, bx is the linear term, and c is the cοnstant term. The cοefficient a determines the shape οf the parabοla, while the cοnstants b and c determine its pοsitiοn and οrientatiοn.
Quadratic functiοns can have οne, twο, οr zerο real rοοts (alsο knοwn as sοlutiοns οr zerοs), which cοrrespοnd tο the x-intercepts οf the parabοla. The number and nature οf the rοοts depend οn the value οf the discriminant, which is given by b² - 4ac.
If the zeroes are x = 2 and x = 5 then the solutions must be:
(x - 2)(x - 5)
Multiply them and make a quadratic function
⇒ (x - 2)(x - 5)
⇒ (x² - 5x)- (2x - 5)
⇒ x² -5x - 2x + 5
⇒ x² -5x - 2x + 5
⇒ x² - 7x + 5
Comparing this to the form of the quadratic function f(x) = ax² + bx + c, we see that a = 1, b = -7, and c = 10. Therefore, the quadratic function with zeros at 2 and 5 is:
f(x) = x²- 7x + 10
So, the correct option is f(x) = x² - 7x + 10.
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There are 410 calories in five ounces of a certain ice cream. How many calories are there in three pounds?
Hence, three pounds of ice cream contain 1968 calories as we can apply a ratio to determine how many calories are contained in 3 pounds .
what is unitary method ?Researchers utilise a method called the unitary approach to tackle proportional issues. It entails identifying a single product value that can be utilized to calculate the values of connected units. The method is predicated on the notion that if the value of one unit of even a quantity is known, then the value of any further unit of the same quantity can be determined. It is frequently employed in the computation of costs, rates, and dimensions.
given
Let's begin by converting 5 ounces to pounds:
A pound weighs 16 ounces.
5 ounces equals 5/16 pounds.
So, we can apply a ratio to determine how many calories are contained in 3 pounds:
(3 pounds/x calories)/5/16 pounds/410 calories
After finding x, we obtain:
3 pounds * 410 calories divided by 5/16 pounds equals 1968 calories.
Hence, three pounds of ice cream contain 1968 calories as we can apply a ratio to determine how many calories are contained in 3 pounds.
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what is the length of ? round to the nearest tenth. group of answer choices 6.8 cm 7.5 cm 14.5 cm 17.7 cm
The calculated length of the segment BC is 14.5 cm
How to calculate the length of the segment BC?From the question, we have the following parameters that can be used in our computation:
The triangle
Using the sine rule, we have
Sin (65)= BC/ 16
So, we have
BC = 16 * sin(65)
When evaluated, we have
BC = 14.5
Hence, the length of the segment BC is 14.5 cm
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What is the answer for this trignometry question?
Answer:
865 m 31.8⁰ south of east
Step-by-step explanation:
R = √456² + 735² = 865 m
∅ = tan⁻¹(-456/735) = -31.8⁰ (31.8⁰ south of east)
i’m circle c, what is the value of x?
The value of x from the triangle inscribed in the circle which is the unknown angle is 22°
Angles of a semicircle Theorem.For a given triangle inscribed in a circle, it should be noted that the angle that is inscribed along the diameter of the circle will be regarded as the right angle.
This means that the angle facing the diameter line (C), i.e angle c is 90 degrees. We all know that the sum of angles in a triangle is 180 degrees. Therefore, to find the third unknown angle x, we have:
x + 68° + 90° = 180°
x + 158° = 180°
x = 180° - 158°
x = 22°
Therefore, we can conclude that the value of x which is the unknown angle is 22°
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Draw a model using integer chips and circle the zero pairs
+----------------+
| 0 | 1 | -1 |
+-----+-----+-----+
| 2 | -2 | 3 |
+-----+-----+-----+
| -3 | 4 | -4 |
+-----+-----+-----+
o o
The zero pairs are (-2, 2) and (-4, 4), and I've circled them in the model above.
To draw a model using integer chips and circle the zero pairs, start by laying out the positive and negative integer chips side by side in a line. The negative numbers should be on the left and the positive numbers should be on the right. Next, take a second line of chips, also with negative numbers on the left and positive numbers on the right, and arrange it so that the chips on the first line line up with the corresponding chips on the second line. For example, the negative 3 chip on the first line should be paired with the positive 3 chip on the second line. The same should be done for all other chips. Finally, circle any pairs of chips where the sum of the two numbers is equal to 0. This will indicate that they are zero pairs.
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Two groups of friends go to a movie. Each ticket costs the same amount. One group spends $57. The other group spends $95. List all possible whole number ticket prices for each group. At most how much does each ticket cost? Suppose a group of 2 friends goes to this movie. At most how much does this group spend?
List all possible whole number ticket prices for the group that spends $57. Select all that apply.
A. $19
B.$1
C. $57
D. $95
E. $3
F. $5
List all possible whole number ticket prices for the group that spends $95. Select all
that apply. A. $3
B. $19
C. $1
D. $57
E. $95
F. $5 At most how much does each ticket cost?
Answer:
1) All possible number tickets for group that spends $57: A, B, C, D
2) All possible number tickets for group that spends $95: B, C, E, F
3) Each ticket will cost at most $19
Step-by-step explanation:
We are told that one group spends $57 dollars while the other group spends $95.
Now,we want to find all possible whole number ticket prices for each group and at most how much each ticket costs.
To do this, let's first find the factors of both amounts which will give us all possible whole number ticket prices for each group.
57: 1, 3, 19, 57
95: 1, 5, 19, 95
Since each ticket costs same amount, to find out at most how much each ticket costs, we will select the highest common factor of both groups which is 19.
Thus,each ticket will cost at most $19
A cow is tethered by a rope 50 m long. The rope is fastened to a hook which is located 10 m from the center on the longer side of barn. The barn measures 60 m by 30 m. Over how much ground can the cow graze? Please, helppp
The cow can graze in the total area of the barn, that is, in 1800m²
How to calculate the area that the cow has available to graze?To calculate the area that the cow has available to graze, we must take into account the following data:
Barn length: 60mBarn width: 30mRope length: 50mHook position: 10m away from the center of the longest part of the barn.According to the above, we must find the area of circumference that the cow tied with the 50m rope can graze.
π × 50m = 157.07m²On the other hand, we find the area of the barn:
60 × 30 = 1800m²According to the above and the graph, it can be inferred that the cow has the ability to graze in the entire barn area.
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HELP ME PLEASE I DON'T UNDERSTAND
Answer:
34/73
Step-by-step explanation:
37 + 34 + 2 = number of customers = 73
73 is our denominator.
34 is the number of people who used a credit card.
34 is our numerator.
Put the two together, and you get 73! Enjoy!
find the missing factor
(2×3)+(2×9)=. (3+9)
Answer: (2*3) = 6
(2*9) = 18 6+ 18 = 24
(3+9) = 12
Step-by-step explanation:
So whats missing is times 2 on the right side next to (3+9) *2
(2×3)+(2×9)=. (3+9)*2
Use the Divergence Theorem to evaluate ∬ S
F⋅NdS and find the outward flux of F through the surface of the solid bounded by the graphs of the equ F(x,y,z)=x 2
i+xyj+zk Q: solid region bounded by the coordinate planes and the plane 3x+4y+6z=24
We obtain the desired result, which represents the outward flux of F through the surface of the solid region bounded by the given coordinate planes and plane equation.
To evaluate the surface integral ∬ S F⋅NdS and find the outward flux of F through the surface of the solid region bounded by the coordinate planes and the plane 3x+4y+6z=24, we can apply the Divergence Theorem.
The Divergence Theorem relates the flux of a vector field F through a closed surface S to the divergence of F over the volume enclosed by S. By calculating the divergence of F and finding the volume enclosed by S, we can compute the desired surface integral and determine the outward flux of F.
The Divergence Theorem states that for a vector field F and a closed surface S enclosing a solid region V, the surface integral ∬ S F⋅NdS is equal to the triple integral ∭ V (div F) dV, where div F represents the divergence of F. In this case, the vector field F(x,y,z) = x^2 i + xy j + zk is given.
To apply the Divergence Theorem, we first need to calculate the divergence of F. The divergence of a vector field F(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k is given by div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In our case, P(x,y,z) = x^2, Q(x,y,z) = xy, and R(x,y,z) = z. Taking the partial derivatives, we have ∂P/∂x = 2x, ∂Q/∂y = x, and ∂R/∂z = 1. Thus, the divergence of F is div F = 2x + x + 1 = 3x + 1.
Next, we need to determine the solid region bounded by the coordinate planes and the plane 3x + 4y + 6z = 24. This plane intersects the coordinate axes at (8,0,0), (0,6,0), and (0,0,4), indicating that the solid region is a rectangular box with sides of length 8, 6, and 4 along the x, y, and z axes, respectively.
Using the Divergence Theorem, we can now evaluate the surface integral ∬ S F⋅NdS by computing the triple integral ∭ V (div F) dV. Since the divergence of F is 3x + 1, the triple integral becomes ∭ V (3x + 1) dV. Evaluating this integral over the volume of the rectangular box bounded by the coordinate planes, we obtain the desired result, which represents the outward flux of F through the surface of the solid region bounded by the given coordinate planes and plane equation.
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There are 12 boys and 15 girls in Mr. Fraioli’s math class. He will randomly call on one person to answer the problem of the day. What is the probability that he will choose a girl
n = 12 + 15 = 27
Probability of choosing girl,
p = 15/27
Probability of choosing boy,
q = 1 - 15/27 = 12/27
\(P(X = 1) = \binom{27}{1} { (\frac{15}{27}) }^{1} ( { \frac{12}{27} )}^{26} \\ = 1.045552364 \times {10}^{ - 8} \)
The probability that he will choose a girl will be equal to 15/27.
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that there are 12 boys and 15 girls in Mr Fraioli’s math class. He will randomly call on one person to answer the problem of the day.
The probability that he will choose a girl,
n = 12 + 15 = 27
Probability of choosing a girl,
p = 15/27
Probability of choosing boy,
q = 1 - 15/27 = 12/27
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Please help! -- Very Easy--
Answer: 60
8x15 / 2
Step-by-step explanation:
Answer:
40 units
Step-by-step explanation:
Using Pythagoras Theorem to find the hypotenuse:
\( \sqrt{ {15}^{2} + {8}^{2} } \)
\( = \sqrt{289} \)
= 17 units
The perimeter
= 15+8+17
= 40 units
A "blink of an eye" is a time interval of about 150 ms for an average adult. The "closure" portion of the blink takes only about 55 ms. Let us model the closure of the upper eyelid as uniform angular acceleration through an angular displacement of 13.4
∘
What is the value of the angular acceleration the eyelid undergoes while closing? rad/s
2
The angular acceleration the eyelid undergoes while closing is approximately 13.93 rad/s².
To find the angular acceleration (α) of the eyelid while closing, we can use the equations of rotational motion. The given data is:
Angular displacement (θ) = 13.4 degrees
Time interval for closure (Δt) = 55 ms = 0.055 s
We can use the following equation to relate angular displacement, angular acceleration, and time:
θ = 0.5 * α * t²
Plugging in the values:
13.4 degrees = 0.5 * α * (0.055 s)²
Let's convert the angular displacement from degrees to radians:
θ = 13.4 degrees * (π/180) radians/degree
θ ≈ 0.2332 radians
Now, we can rearrange the equation to solve for α:
α = (2θ) / (t²)
α = (2 * 0.2332 radians) / (0.055 s)²
Calculating the value:
α ≈ 13.93 radians/s²
Therefore, the angular acceleration the eyelid undergoes while closing is approximately 13.93 rad/s².
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So far in Unit 3, we have studied several hypothesis tests: 1-Prop z-Test, 2-Prop z-Test, 1-Sample t-Test, 2-Sample t-Test, and the Paired t-Test. For each scenario, identify the hypothesis test that should be applied. (1 point each) a. A researcher wants to test a claim that the average pounds of grapes on unfertilized vines decreases the yield of each grapevine when compared to the average pounds of grapes on fertilized vines. b. A researcher wants to test a claim that the average amount of time that kids spend reading books has decreased. c. A researcher wants to test a claim that students perform better on math problems when not listening to music as compared to when they do listen to music. d. A researcher wants to test a claim that the average age of professional baseball players is higher than the average age of professional football players. e. A researcher wants to test a claim that the proportion of children with autism has increased since 1990. f. A researcher wants to test a claim that there is a difference between the proportion of immigrants in the US and Canada.
a. The appropriate hypothesis test for this scenario would be a 2-Sample t-Test, as we are comparing the average pounds of grapes on unfertilized vines to the average pounds of grapes on fertilized vines.
b. The appropriate hypothesis test for this scenario would be a 1-Sample t-Test, as we are comparing the average amount of time kids spend reading books to a known or assumed value.
c. The appropriate hypothesis test for this scenario would be a Paired t-Test, as we are comparing the performance of the same students on math problems with and without music.
d. The appropriate hypothesis test for this scenario would be a 2-Sample t-Test, as we are comparing the average age of professional baseball players to the average age of professional football players.
e. The appropriate hypothesis test for this scenario would be a 1-Prop z-Test, as we are testing the proportion of children with autism.
f. The appropriate hypothesis test for this scenario would be a 2-Prop z-Test, as we are comparing the proportions of immigrants in the US and Canada.
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Show that the Laplace transform of
dx
dy
, i.e L(
dx
dy
)=sL(y)−y(0) or L(
dx
dy
)=sY−y(0). ii. Then deduce the Laplace transform of
dx
4
d
4
y
, i.e L(
dx
4
d
4
y
).
The Laplace transform of dx/dy is sL(y) - y(0) / y or sY - y(0), and the Laplace transform of \(dx^4/dy^4\) is \((sL(y) - y(0) / y)^4\).
The Laplace transform is a mathematical tool used to convert a function of time into a function of complex frequency, known as the Laplace domain.
To show that the Laplace transform of \(dx/dy\) is \(sL(y) - y(0)\) or\(sY - y(0)\), we can apply the definition of the Laplace transform.
Let's start by finding the Laplace transform of dx/dy.
\(L(dx/dy)\) = ∫\((e^(-st) * dx/dy) dt\)
Using integration by parts, we can rewrite this as:
\(L(dx/dy) = e^(-st) * x/y -\) ∫\(((d/dt)(e^(-st) * x/y) dt)\)
\(L(dx/dy) = e^(-st) * x/y - s *\)∫\((e^(-st) * x/y) dt\)
Now, we can write this as:
\(L(dx/dy) = e^(-st) * x/y - s * L(x/y)\)
But L(x/y) is simply L(y) / L(x), so we can substitute this in:
\(L(dx/dy) = e^(-st) * x/y - s * (L(y) / L(x))\)
Rearranging this equation, we get:
\(L(dx/dy) = sL(y) - (1/y) * L(x)\)
Since L(x) is a constant (given the initial condition x(0)), we can rewrite this as:
\(L(dx/dy) = sL(y) - y(0) / y\)
Hence, the Laplace transform of dx/dy is sL(y) - y(0) / y or sY - y(0).
Now, let's deduce the Laplace transform of\(dx^4/dy^4\).
Using the linearity property of the Laplace transform, we can rewrite this as:
\(L(dx^4/dy^4) = L(dx/dy * dx^3/dy^3)\)
Applying the property that L(dx/dy) = sL(y) - y(0) / y, we get:
\(L(dx^4/dy^4) = (sL(y) - y(0) / y) * L(dx^3/dy^3)\)
Now, we can continue applying the property for L(dx/dy) to the remaining term \(L(dx^3/dy^3)\):
\(L(dx^4/dy^4) = (sL(y) - y(0) / y) * [(sL(y) - y(0) / y) * L(dx^2/dy^2)]\)
Repeating this process, we finally obtain:
\(L(dx^4/dy^4) = (sL(y) - y(0) / y)^4\)
Therefore, the Laplace transform of \(dx^4/dy^4 is (sL(y) - y(0) / y)^4.\)
In summary, the Laplace transform of dx/dy is sL(y) - y(0) / y or sY - y(0), and the Laplace transform of \(dx^4/dy^4 is (sL(y) - y(0) / y)^4.\)
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Solve the following quadratic equation, leaving your answer in exact form:
4e^2 - 15e = -4
e =
or e =
The solution of the quadratic equation 4e² - 15e = -4 in the exact form is e = (15 + √161)/8 or e = (15 - √161)/8
To solve the quadratic equation 4e² - 15e = -4, we can rearrange it into standard form as follows,
4e² - 15e + 4 = 0. We can then use the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions are given by,
x = (-b ± √(b² - 4ac)) / 2a
Applying this formula to our equation, we have,
e = (-(-15) ± √((-15)² - 4(4)(4))) / 2(4)
Simplifying this expression, we get,
e = (15 ± √(225 - 64)) / 8
e = (15 ± √161) / 8
Therefore, the solutions to the equation 4e² - 15e = -4 are:
e = (15 + √161) / 8 or e = (15 - √161) / 8
These are exact solutions in radical form.
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What’s the measure of Please help I need this ASAP
Answer:
the answer is 124 degrees my friend
How to find the discount
determine if all polynomial of the form p(t) = a t^2, where a is in r, is a subspace of p2
The set satisfies all three requirements, we can conclude that all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2. To determine if all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2,.
We need to check if it satisfies the three requirements of a subspace:
1. The zero vector is in the set.
2. The set is closed under addition.
3. The set is closed under scalar multiplication.
First, let's check if the zero vector is in the set. The zero vector of p2 is the polynomial 0t^2 + 0t + 0, which can be written as p(t) = 0. To see if p(t) = 0 is in the set of polynomials of the form p(t) = a t^2, we need to check if there exists an "a" that satisfies p(t) = a t^2 = 0 for all values of t. This is true only if a = 0, so the zero vector is in the set.
Next, let's check if the set is closed under addition. Suppose we have two polynomials p(t) = a t^2 and q(t) = b t^2, where a and b are in r. Then, their sum is p(t) + q(t) = a t^2 + b t^2 = (a+b) t^2. This is also of the form p(t) = a t^2, where a = a+b, so it is in the set. Therefore, the set is closed under addition.
Finally, let's check if the set is closed under scalar multiplication. Suppose we have a polynomial p(t) = a t^2, where a is in r, and a scalar k. Then, k * p(t) = k * a t^2 = (ka) t^2. This is also of the form p(t) = a t^2, where a = ka, so it is in the set. Therefore, the set is closed under scalar multiplication.
Since the set satisfies all three requirements, we can conclude that all polynomials of the form p(t) = a t^2, where a is in r, is a subspace of p2.
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Which system of linear equations represents the situation?
The Martin family pays $12 per hour to a babysitter. They also give her
a $7 tip. The Bagley family pays $15 per hour to a babysitter. The
Bagley family's babysitter pays $8 to order a pizza.
Let h represent the number of hours of babysitting and m represent
the total amount of money each babysitter earns.
Answer:
so many just add them 12+7+15+8=
Answer:
m=12h+7
m=15h-8
If a pet grooming salon hires an additional groomer, that worker can groom 4 additional pets per day. the average grooming fee is $25. the most the salon would be willing to pay that groomer is
The most the salon would be willing to pay that groomer is $25×4 = $100.
What is unitary method?The unitary method is a technique that determines the worth of a single unit from value of multiple units, as well as the quality of multiple units from value of a single unit.
Some key features regarding the unitary method are-
It's a method which we use for the majority of math calculations. This method will come in handy when answering questions about ratio & proportion, algebra, geometry, and other subjects.We can determine the missing value using the unitary method. For example, if one carton of juice pays $5, how much would five such packets cost? We can then easily determine the price of 5 packets, which is $25.To know more about the unitary method, here
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how do i solve this
4x-9=7x+12
Answer:
x = -7
Step-by-step explanation:
4x - 9 = 7x + 12
~Add 9 to both sides
4x = 7x + 21
~Subtract 7x to both sides
-3x = 21
~Divide -3 to both sides
x = -7
Best of Luck!
Answer:
x = -7
Step-by-step explanation:
Combine like terms: (Subtract 4x from both sides, and subtract 12 from both sides)
4x - 9 = 7x + 12
-9 - 12 = 7x - 4x
-21 = 3x
Divide by 3:
-21 = 3x
x = -21 / 3
x = -7
Plug in to check your answer:
4x - 9 = 4(-7) - 9 = -37
7x + 12 = 7(-7) + 12 = -37
HELPPP PLEASE please
Answer:
1
Step-by-step explanation:
any number to the power of 0 is 1
8^0 = 1
1009934^0 = 1
Please please please help
An open cylindrical water tank has base radius x metres and height h metres. Each square metre of the
base costs a dollars to manufacture and each square metre of the curved surface costs b dollars. The
combined cost of the base and curved surface is c dollars.
a Find c in terms of a, b, x and h.
X
b
Show that the volume of the tank is given by V = -(c – παχ2).
2b
c As x varies, prove that V is at its maximum when the cost of the base is dollars.
3
V is at its maximum when \(a = b\ \pi x\), \(V = \pi x2h\), and \(c = a x2 + b\ \pi xh\).
Determine the cost of the tank.This question uses the principles of geometry, specifically the formulas for the area of a circle and the area of a curved surface. In addition, the concept of cost maximization is used to determine the cost of the tank when the volume is at its maximum.
Given,
\(c = a x2 + b\ \pi xh\)
This equation states that the cost of the tank is equal to the cost of the base plus the cost of the curved surface.
The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.
The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.
The area of the curved surface is equal to πxh, where h is the height of the tank.
Combining these two equations gives the equation for c.
\(V = \pi x2h\)
This equation states that the volume of the tank is equal to the area of the base multiplied by the height.
The area of the base is equal to \(\pi x2\), where x is the radius of the base. The height of the tank is h. Combining these two equations gives the equation for V.
V is at its maximum when \(a = b\pi x\)
This equation states that the volume of the tank is maximized when the cost of the base is equal to the cost of the curved surface.
The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.
The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.
The area of the curved surface is equal to πxh, where h is the height of the tank.
Setting a equal to bπx gives the equation for the maximum volume.
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jurgen is twice as old as francine, who is 8 years old. add their ages, subtract 6, and divide by 3. what is the result?
Answer:
answer is 6
Step-by-step explanation:
jurgen is twice as old as francine, means jurgen is 8*2 = 16 years old.
adding their ages: 16 + 8 = 24
subtracting 6: 24 - 6 = 18
dividing by 3: 18/3
answer: 6