The table shows the number of correct answers on a practice standardized test. You score 86 points on the test, and your friend scores 76 points. How many points is each type of question worth?

Answer:

Lucas

Step-by-step explanation:

Katie's response would mean that no matter how many ants there are, there will only always be 6 legs, which is incorrect.

Lucas's response would mean that the number of ants would equal the total number of legs divided by 6, which is correct.

The average height increase for each additional centimeter in arm spam is 6.4 cm

Given the Linear regression equation :

The general equation for a linear trendline is :

b = slope or gradient which is the change in x -vakue per Change in y-value.

comparing the equations, the slope of the relationship is 6.4 .

Therefore, for each additional centimeter of arm spam, the average height increase is 6.4 cm.

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The dot product between the vectors \( u = a\mathbf{i} + b\mathbf{j} \) and \( v = \mathbf{i} - b\mathbf{j} \) is \( a^2 - b^2 \).

To find the dot product between two vectors, we multiply their corresponding components and then sum them up.

Let's calculate the dot product between  \( u \) and \( v \):

\( u \cdot v = (a\mathbf{i} + b\mathbf{j}) \cdot (\mathbf{i} - b\mathbf{j}) \)

Expanding the dot product, we have:

\( u \cdot v = a\mathbf{i} \cdot \mathbf{i} + a\mathbf{i} \cdot (-b\mathbf{j}) + b\mathbf{j} \cdot \mathbf{i} + b\mathbf{j} \cdot (-b\mathbf{j}) \)

Since \( \mathbf{i} \) and \( \mathbf{j} \) are orthogonal unit vectors, their dot products with themselves are equal to 1, and their dot product with each other is equal to 0:

\( \mathbf{i} \cdot \mathbf{i} = 1 \)

\( \mathbf{i} \cdot \mathbf{j} = 0 \)

\( \mathbf{j} \cdot \mathbf{j} = 1 \)

Simplifying the dot product of \( u \) and \( v \):

\( u \cdot v = a(1) + a(0) + b(0) + b(1) = a + b \)

Therefore, the dot product between u and v is a + b.

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The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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The rate at which the diameter decreases is  -0.16cm/min

Diameter:

In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.

Given,

Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.

Here  we obtained the equation that relates the surface area S and the diameter D of a sphere given by

=> S = πD²

Now, we have differentiate the equation as,

=> dS/dt = d/dt (πD²)

=> dS/dt = π d/dt (D²)

​=> dS/dt = 2πD dD/dt

Now, Solving for dD/dt, which is the unknown for this problem, we have

=> dD/dt ​= 1/2πD​ x dS​/dt

Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is

=> dD/dt = 1/2 x π x 10 (-1)

=> dD/dt = -1/20π

=> dD/dt = -0.16cm/min

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Answer:

not a sloution

Step-by-step explanation:

93÷6 is 15.5 not 15 w=15.5

The choice which provides the best evidence for the answer to the previous question is Lines 53-57 ("As the . . . consciousness").

Given a passage as shown in the attached images.

Option D is the best answer. The previous question asks what connection the narrator draws between Eppie and Silas. The answer, that as she learns more about the world, he becomes more involved in it. awareness.

Alternatives to D as A, B, and C are incorrect because the quoted lines do not support an answer to the previous question about 's link between Eppie and Silas, instead objecting to Silas locating gold with Eppie's curiosity (options A)  and describing Silas’s habitual behavior when accompanying Eppie outdoors (options B and C).

Hence, the choice which provides the best evidence for the answer to the previous question from the given passage is Lines 53-57 ("As the . . . consciousness").

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The complement of an angle is 50 more than the measure of the angle are 20 and 70 degrees.
Two angles are said to be complimentary if their sum is 90 degrees.

We have two angles, x and x+50 more than its complement, so we can write:

Let the first angle be x.

Let the second angle be x+50.

x+ x + 50 = 90
2x +50 = 90

2x = 90-50

2x = 40

x = 20

The first angle is 20 degrees.
the second answer is x+50= 20+50= 70 degrees.

Both angle measures are 20 and 70.
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Answer:

1571862.11penny

Step-by-step explanation:

The formula for calculating the compound interest is expressed as;

A = P(1+r/n) ^nt

Given

Principal P = $5000

r is the rate = 8.25% = 0.0825

t is the time = 15 years

n is the time of compounding = 6/12 = 1/2

Substitute

A = 5000(1+0.0825/0.5)^0.5(15)

A = 5000(1+0.165)^7.5

A = 5000(1.165)^7.5

A = 5000(3.1437)

A = 15,718.6

hence the amount of money in the account after 15years is $15,718.6211 which is 1571862.11penny

Answer:

Answer is B

Step-by-step explanation:

Answer:

IT is B

Step-by-step explanation:

a.  The mapping for this outcome is (2, 3) → 5.

b. The tight range of X is [2, 12]. c. X⁻¹(12) = {(6, 6)}

d. The strict range of X⁻¹ is the sample space S itself.

a. To map the members of S with X to S', we need to determine the possible values of X for each outcome in the sample space S. In this case, the sample space S consists of all possible outcomes when rolling two balanced dice.

The sample space S can be represented as a set of ordered pairs (x, y), where x and y represent the numbers appearing on each of the two dice. Since each die has six sides numbered from 1 to 6, the sample space S contains 36 possible outcomes, which can be listed as follows:

S = {(1, 1), (1, 2), (1, 3), ..., (1, 6), (2, 1), (2, 2), ..., (6, 6)}

Now, we define the point function X, which represents the number of numbers on the side of the die that appears. The values of X can range from 1 to 6, since those are the possible numbers on a die. To map the members of S to S', we determine the sum of the numbers on each outcome in S and assign it to X. Mathematically, this can be expressed as:

X((x, y)) = x + y

For example, if we consider the outcome (2, 3) from the sample space S, we calculate X((2, 3)) = 2 + 3 = 5. So, the mapping for this outcome is (2, 3) → 5.

b. The tight range of X represents the set of all possible values that X can take. In this case, X represents the sum of the numbers appearing on the two dice. The minimum sum occurs when both dice show the number 1, so the smallest possible value for X is 1 + 1 = 2. Similarly, the maximum sum occurs when both dice show the number 6, so the largest possible value for X is 6 + 6 = 12.

Therefore, the tight range of X is [2, 12].

c. To build the inverse function X⁻¹, we need to determine the pre-image of each value in the range of X. In this case, the range of X is the set of positive integers less than 14 (S'). We consider each possible value of X and find the corresponding outcomes in the sample space S.

For example, for X = 2, the possible outcomes in S are (1, 1). Similarly, for X = 3, the possible outcomes in S are (1, 2) and (2, 1). We continue this process for each value of X from 2 to 12.

The inverse function X⁻¹ can be represented as a mapping from S' to the set of outcomes in S. Here is the mapping for each value of X:

X⁻¹(2) = {(1, 1)}

X⁻¹(3) = {(1, 2), (2, 1)}

X⁻¹(4) = {(1, 3), (2, 2), (3, 1)}

X⁻¹(5) = {(1, 4), (2, 3), (3, 2), (4, 1)}

X⁻¹(6) = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

X⁻¹(7) = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

X⁻¹(8) = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

X⁻¹(9) = {(3, 6), (4, 5), (5, 4), (6, 3)}

X⁻¹(10) = {(4, 6), (5, 5), (6, 4)}

X⁻¹(11) = {(5, 6), (6, 5)}

X⁻¹(12) = {(6, 6)}

d. The strict range of X⁻¹ represents the set of all possible values that X⁻¹ can take. In this case, the strict range is the set of outcomes in S for which X⁻¹ is defined.

The strict range of X⁻¹ consists of all the outcomes from the sample space S. Each outcome in S corresponds to a unique value in the range of X, so X⁻¹ is defined for all outcomes in S.

Therefore, the strict range of X⁻¹ is the sample space S itself.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

3

Step-by-step explanation:

substitute x = 4 , y = 6 into the expression

y - (5 - (x - y))

= 6 - (5 - (6 - 4))

= 6 - (5 - 2))

= 6 - 3

= 3

Answer:

-55/8

Hope this helps! :)

The least distance traveled is \($240\sqrt{3}$\) feet.

Each boy shakes hands with the two boys who are not adjacent to him on the circle. Since there are six boys in total, each boy shakes hands with four other boys. We can represent these handshakes on a graph, where the six vertices represent the six boys and the edges represent the handshakes. Each vertex has degree 4, meaning that there are 12 edges in total.

To minimize the distance traveled, each boy should simply walk directly across the circle to shake hands with the two boys on the opposite side. This way, each boy walks a distance equal to the diameter of the circle, which is \(2 \times 40 = 80$ feet.\)

Since there are six boys, the total distance traveled is \(6 \times 80 = 480$ feet\). However, we have counted each handshake twice, so we need to divide by 2 to get the total distance traveled. This gives us \(240$ feet.\)

To express this answer in the simplest radical form, we can use the fact that an equilateral triangle with side length \(s$\) has height \(s\sqrt{3}/2$\). The six handshakes form an equilateral triangle with side length 80, so its height is \(80\sqrt{3}/2 = 40\sqrt{3}$ feet\). Therefore, the total distance traveled is \(240\sqrt{3}$\) feet.

Therefore, the correct answer is \(240\sqrt{3}$\)feet.

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the set \($B \times C$\) can be written using roster notation as \(\{(foam, non$-$fat),\) (foam, whole), \((no$-$foam, non$-$fat), (no$-$foam, whole)\}$\)

We can write \($A \times B \times C$\) as the set of all ordered triples \($(a, b, c)$\), where \(a \in A$, $b \in B$ and $c \in C$\). One such example of an element in this set can be \(($tall$, $foam$, $non$-$fat$)\).

Thus, one element from the set

\(A \times B \times C$ is ($tall$, $foam$, $non$-$fat$).\)

We can write \($B \times A \times C$\) as the set of all ordered triples \((b, a, c)$, where $b \in B$, $a \in A$ and $c \in C$\).

One such example of an element in this set can be \((foam$,  $tall$, $non$-$fat$)\).

Thus, one element from the set \(B \times A \times C$ is ($foam$, $tall$, $non$-$fat$)\).

We know \(B = \{foam, no$-$foam\}$ and $C = \{non$-$fat, whole\}$\).

Therefore, \($B \times C$\) is the set of all ordered pairs \((b, c)$, where $b \in B$ and $c \in C$\).

The elements in \($B \times C$\) are:

\(B \times C = \{&(foam, non$-$fat), (foam, whole),\\&(no$-$foam, non$-$fat), (no$-$foam, whole)\}\end{align*}\)

Thus, the set \($B \times C$\) can be written using roster notation as \(\{(foam, non$-$fat),\) (foam, whole), \((no$-$foam, non$-$fat), (no$-$foam, whole)\}$\).

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Answer:

This is a type of statistical inference known as a measure of center

Answer:

There you go , happy to help

Let the number of free throws Jeramiah got be x and the field goals he got be 17-x.

x + 2(17-x) = 28

x = 6

Jeramiah made 6 field throws.

Answer:

Total distance from the ship(Base) = 26,167 (Approx)

Step-by-step explanation:

Given:

Height of helicopter from sea (Height) = 8,000 m

Angel = 17°

Find:

Total distance from the ship(Base)

Computation:

⇒ Total distance from the ship(Base) = Height of helicopter from sea (Height) / Tan 17°

Total distance from the ship(Base) = 8,000 / 0.3057

⇒ Total distance from the ship(Base) = 26,167 (Approx)

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

Answer:

Pretty sure it's c)

Answer:

Step-by-step explanation:

The most likely quantity is centimetres.

The second option can be inches.

Hope this helps

plz mark it as brainliest!!!!!!!!!

Answer:

To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:

4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5

So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.

Step-by-step explanation:

The congruent triangles in this problem are given as follows:

Triangles A and B.

Two figures are classified as congruent if their side lengths are the same.

If we rotate triangle B 180º over it's base, we have that it will have a similar format to triangle A, and also with the same side lengths.

Hence the congruent triangles in this problem are given as follows:

Triangles A and B.

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There are 7

Seven zeros in one crore

The one crore implies ten million.

Answer:

12.5 hours a week

Step-by-step explanation:

So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?

10 hours = 80%

80% = 0.8

10/0.8 = 12.5 hours a week