Find the measures of the angles 1 through 7.

Answer:

Age of Lee = y years

Age of Toby = (y - 8) years

Sum of their ages < 41

or, y +y - 8 < 41

or, 2y - 8 < 41

Adding '8' on both sides,

or, 2y - 8 + 8 < 41

or, 2y < 41

Answer:

We know that:

1/5 = 0.2 of all adults in US have type O blood.

Then: 4/5 = 0.8 of all adults in US do not have type O blood.

a)  All four are type O.

Let's think this, as four events with two possible outcomes, having type O blood, with a probability of 0.2, and not having type O blood with a probability of 0.8

Now if we want the four people to have type O blood, then we have the outcome with probability 0.2 four times, and as we know, the joint probability is equal to the product of the individual probabilities:

P  =0.2^4 = 0.0016

b) None of them is type O.

Similar to the above case, but this time we work with four times the probability 0.8

P = 0.8^4 = 04096

c) Two of the four are type O.

Here we will have two times the probability 0.2, and two times the probability 0.8.

p = 0.2^2*0.8^2

But, if the people is ordered, the two persons with type O blood can be:

first and second

first and third

first and fourth.

second and third

second and fourth

third and fourth.

6 different combinations, then the actual probability for this case will be:

P = 6*p = 6*(0.2^2*0.8^2) = 0.1536

The probability of All four are type O, None of them is type O, and Two out of the four are type O is 0.0016, 0.4096, and 0.0256 respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

About 1/5 of all adults in the United States have type O blood.

p = 0.2

q = 1 - p = 1 - 0.2 = 0.8

a. All four are type O. The probability will be

P = p⁴  

P = 0.2⁴

P = 0.0016

b. None of them is type O. The probability will be

P = q⁴  

P = 0.8⁴

P = 0.4096

c. Two out of the four are type O. The probability will be

P = p² × q²  

P = 0.2² × 0.8²

P = 0.04 × 0.64

P = 0.0256

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Answer:

It is 5/6

Step-by-step explanation:

For questions like these use caculator soup you can use it for fractions and much more it shows u how to work the problem out also.

Answer: 2

Step-by-step explanation:

we simply plug in 2 for y.

3(2) - 4

6 - 4

6 - 4 = 2

Answer:

3y-4=2

3×2-4

=6-4

2 the value of y is 2

Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

If 58% = 58÷100 of the people have been vaccinated, then;

1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.

Now:

Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;

P( > 1 ) = 1 - P(0)                 -----------(1)

Where;

P(0) = probability that all of the four have not been vaccinated.

P(0) = P(1) x P(2) x P(3) x P(4)×p(5)

Where;

P(1) = Probability that the first out of the four has not been vaccinated

P(2) = Probability that the second out of the four has not been vaccinated

P(3) = Probability that the third out of the four has not been vaccinated

P(4) = Probability that the fourth out of the four has not been vaccinated

P(5)=Probability that the fifth out of the five has not been vaccinated

Remember that 42÷100 of the population has not been vaccinated. Therefore,

P(1) = 42÷100    

P(2) = 42÷100

P(3) = 42÷100

P(4) = 42÷100

P(5)=42÷100

P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)

P(0) = (42÷100)⁵

P(0) = (0.42)⁵

P(0) = 0.013067

Therefore, from equation (1);

P( > 1 ) = 1 -0.013067

P( > 1 ) = 0.98693

Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

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Answer:

1. Adrian would have to pay a total of $90 for him and his family if they were to also buy five snacks.

2. The equation for the next question would be y = 4x + 70, where y is total cost and x is the amount of snacks being bought.

Step-by-step explanation:

Adrian would have to pay $90 for movie tickets and 5 snacks for his family. The cost of snacks would be the number of snacks multiplied by $4.

In order to calculate the total cost of movie tickets and snacks, we need to consider the number of movie tickets and snacks being purchased. Adrian is taking 4 kids with him, so he needs to buy 5 movie tickets in total. Each movie ticket costs $14, so the total cost for movie tickets is 5 x $14 = $70.

If Adrian is buying 5 snacks for everyone to share, the cost of snacks would be 5 x $4 = $20. Therefore, the total cost for movie tickets and 5 snacks would be $70 + $20 = $90.

If Adrian were to buy xx snacks, the cost of snacks would be xx x $4 = $xx.

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Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

\(\frac{1}{10} \£\)

Step-by-step explanation:

We know that £1 equals 100p.

Knowing this relation, we can use the rule of three

\(30p \times \frac{ \£1}{100p} =0.3 \£\)

Then, we form the fraction

\(\frac{0.3 \£}{\£ 3.00} =\frac{3}{30} =\frac{1}{10} \£\)

Therefore, the fraction of of £3.00 is

\(\frac{1}{10} \£\)

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

Step-by-step explanation:

The given relations can be used to describe each of the numbers in terms of how many Lisa served. Those can then be related by the total served.

__

Let L represent the number of orders Lisa served. Chau served 8 fewer, so (L -8). Austin served 4 times as many, so (4L). The total served was ...

  L +(L -8) +4L = 124

  6L = 132 . . . . . . . . add 8, combine terms

  L = 22 . . . . . . . . divide by 6

  L -8 = 22 -8 = 14 . . . the number Chau served

  4L = 4(22) = 88 . . . the number Austin served

The numbers each served were ...

Answer:

Jackie

Step-by-step explanation:

Since Grace charges 30 an hour (540 divided by 18 is 30) and Jackie charges 40 and hour, so Jackie would charge more.

Answer:

Rectangular pyramid and triangular pyramid

Step-by-step explanation:

A rectangular pyramid and triangular pyramid has the same number of faces as vertices

A pyramid is a three dimensional shape (has length, width and height) with a polygonal base and flat triangular faces.

A rectangular pyramid have same number of faces as vertices with each being 5 in number. A triangular pyramid have same number of faces as vertices with each being 3 in number.

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Answer:

is there any whole number or decimal

The square feet of paper that will cover the model is 56 ft squared.

The model above is a square base pyramid. Therefore, the square feet of papers he will need to cover the model is the surface area of the model.

Therefore,

surface area of the square base pyramid = A + 1 / 2 ps

where

Therefore,

p = 4 × 4 = 16 ft

s = 5 ft

A = 4² = 16 ft²

Therefore,

surface area of the square base pyramid = 16 + 1 / 2 × 16 × 5

surface area of the square base pyramid = 16 + 40

surface area of the square base pyramid = 56 ft²

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The maximum possible cost of a portion of fish is £4.

The cost of a product or service is the amount of money spent on it. It is the whole cost of purchasing, manufacturing, or producing something. The cost of a work may also refer to the amount of time and effort required to finish it. When determining whether or not to buy a product or service, cost is a crucial consideration, and it may be influenced by a number of variables such as material prices, labor expenses, overhead, and demand.

A piece of fish can cost no more than £4.

We may use the following equation to figure this out:

5 servings of fish at £f each + 2 bags of chips at £2 each = £20

This equation may then be rearranged to solve for f:

f = (20 - (2 x 2))/5

f = 16/5

f = £3.20

As a result, the most a slice of fish may cost is £4.

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Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

\(y = f(x)\)

To find the area under the curve \(y = f(x)\) between \(x = a\) and \(x = b\), all we need is to integrate \(y = f(x)\) between the limits of \(a\) and \(b\).

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

\(A=\int _a^b|f\left(x\right)|dx\)

    = \(\int _{-2}^2\left|x^2-4\right|dx\)

\(\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\)

   \(=\int _{-2}^2x^2dx-\int _{-2}^24dx\)

solving

\(\int _{-2}^2x^2dx\)

\(\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\)

   \(=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}\)

    \(=\left[\frac{x^3}{3}\right]^2_{-2}\)

computing the boundaries

     \(=\frac{16}{3}\)

Thus,

\(\int _{-2}^2x^2dx=\frac{16}{3}\)

similarly solving

\(\int _{-2}^24dx\)

\(\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax\)

     \(=\left[4x\right]^2_{-2}\)

computing the boundaries

      \(=16\)

Thus,

\(\int _{-2}^24dx=16\)

Therefore, the expression becomes

\(A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx\)

  \(=\frac{16}{3}-16\)

  \(=-\frac{32}{3}\)

  \(=-10.67\) square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

Answer:

First one is b second one is a thrid is c

Step-by-step explanation:

Given parameters:

   Coordinates of the points =  (3,4) and (19, 16)

Unknown:

The distance between the points = ?

The midpoint  = ?

Solution:

  The distance between two points can be mathematically solved using;

    D  = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }\)

 where  x₁  = 3, x₂  = 19  and y₁  = 4, y₂  = 16

Input the parameters and solve;

   D  = \(\sqrt{(19 - 3)^{2} + (16 - 4)^{2} }\)   = 20

Midpoint;

    The expression is given as;

     x\(_{m}\) , y\(_{m}\)  = \(\frac{x_{1} + x_{2} }{2}\)  , \(\frac{y_{1} + y_{2} }{2}\)

         input the parameters and solve;

                   = \(\frac{3 + 19}{2}\)  , \(\frac{4 + 16}{2}\)

                   = 11 , 10

The midpoint is (11, 10)

Answer:

Terms:

1) = 7/3

2) = -7/9

3) = 7/27

4) = -7/81

Step-by-step explanation:

Your question did not state the equation of f(x), however; assuming f(x) = 7/(1+x)  ,....... at  a = 2

see solution attached then use it to work your f(x)

Given :

Vector V has components of (6,9).

To Find :

The angle in degrees that vector V makes with the x-axis.

Solution :

The x-component of vector is, x = 6 units.

The y-component of vector is, y = 9 units.

So, the angle the vector makes from the horizon is :

\(\theta = tan^{-1}{\dfrac{y}{x}}\\\\\theta = tan^{-1}{\dfrac{9}{6}}\\\\\theta = 56.31^o\)

Hence, this is the required solution.

Answer:

(x - 5) (x - 4)

x(x - 4) - 5(x -4)

x^2 - 4x - 5x - 20

x^2 - 9x - 20

Expand: x (x - 4) - 5 (x - 4)

Simplify: x^2 - 9x - 20

Answer: 69.8°F

Step-by-step explanation:

Answer:

1/4 of the gallon

Step-by-step explanation:

3/4 x 1/3 = 3/12 = 1/4

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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The length of AB is AB = 8 units.

What is distance between two points?

The length of a straight line in the coordinate plane that connects two points in space is what is referred to as their distance. We use the absolute value to calculate the distance between any two points because it is impossible for this distance to be negative.

Consider, the given points A (-4, -3), B (4, -3), C (4, -7), D (-4, -7).

We have to find the length of AB.

Consider, the distance formula,

\(d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}\)

where,

\((x_1, y_1)\) and \((x_2, y_2)\) are the points.

Here,

\((x_1, x_2) = (-4, -3)\\(x_2, y_2) = (4, -3)\)

Plug these values in the above formula,

\(d = \sqrt{(4-(-4))^2+(-3-(-3))^2} \\d = \sqrt{8^2 +0^2} \\d = \sqrt{8^2} \\d = 8\)

Hence, the length of AB is AB = 8 units.

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Answer: 5/24

Step-by-step explanation:

(-2/3)+(7/8)=

(-2/3)+(7/8)*24/24=        ==> 24 is the LCM of 3 and 8

\(\frac{(-2*24)/3+(7*24)/8}{24}\)=

\(\frac{-2*24/3+7*24/8}{24}\)=

\(\frac{-2*8+7*3}{24}\)=

\(\frac{-16+21}{24}\)=5/24

In this problem, we have that the graph in fact represents a function, as there are no vertically aligned points, that is, each input is mapped to a single output.

For a linear function, as is the case for this problem, both the domain and the range will always be represented by all real numbers.

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