13. The cost of 7 shirts and 3 pairs of trousers is shs. 2950 while that of 5 pairs of trousers and 3 shirts is less by 200. How much will Dan pay for 2 shirts and 2 pairs of trousers? 14 A father is twice as old as his​

Answer: 4.2

Step-by-step explanation: First, you'd need to re-arrange the decimals so, you can get 4.65.........

Then, you round up to get about 4.7

Another way is to round up the decimals, so your new equation:

[tex]\frac{21}{5}[/tex]

Then, you'd divide to get 4.2. This way is more of an estimate than the 1st way; the 1st way is an exact answer [rounded] I hope this helped.

Answer:

  4.64

Step-by-step explanation:

You want an estimate of the quotient 21.4/4.6.

Multiplication and division by 5 are simplified by the relation ...

  5 = 10/2

Here, the denominator is about 5, so the quotient is about ...

  21.4 × 2/10 = 42.8/10 = 4.28 ≈ 4.3 . . . . . a first estimate; known to be low

We notice that 4.6 is 0.4 less than 5, which is 0.8/10 = 0.08, or 8% less. That means the actual quotient will be on the order of 8% more than 4.3.

A closer estimate would be ...

  4.3 + 0.08 · 4.3 = 4.3 +0.344 ≈ 4.64

An estimate of the quotient is 4.64.

__

Additional comment

To compute our "error correction," we rounded 4.28 up to 4.3, about 2 parts in 400, making that number (4.3) be about 0.5% high. The estimate of 1/0.92 ≈ 1.08 turns out to be about 0.7% low. This means an even better estimate would add 0.2%, or about 0.009, to the estimate we have, making it about 4.653. These second-order corrections are also slightly off. The actual quotient rounds to 4.652.

Doubling a number is so easy that we elected to keep all of the digits of the numerator when we did the division by 5. This gave a more satisfying 4.3 instead of 4 as the first estimate.

On solving the provided question we can say that the polynomial is x² + 6x + 8  by factorization are x(x-5) - 1(x-5) ⇒ (x-1)(x-5) ⇒ x = 5, 1

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x2 – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the polynomial is

by factorization are

x(x-5) - 1(x-5)

(x-1)(x-5)

x = 5, 1

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Answer:

1000

Step-by-step explanation:

\log _{10}\left(5\right),\:500,\:2\log _{10}\left(5\right),\:2+\log _{10}\left(4\right),\:32+\log _{10}\left(4\right),\:8

A student at Big Sky Middle School are more likely to get a t-shirt than a student at High Peaks High School.

(a) To calculate the probability of getting a t-shirt if you are a student at the middle school, we divide the number of t-shirts being given away by the number of students at the school.

Probability of getting a t-shirt at the middle school = 40 / 350 = 4/35 = 0.114 or 11.4%.

(b) To calculate the probability of getting a t-shirt if you are a student at the high school, we divide the number of t-shirts being given away by the number of students at the school.

Probability of getting a t-shirt at the high school = 75 / 800 = 3/32 = 0.094 or 9.4%.

(c) From the above calculations, it is clear that you are less likely to get a t-shirt if you are a student at the high school (9.4%) than at the middle school (11.4%).

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Based on the information provided and the discount, Nick will pay a total of $36 for the sweater.

The discount is defined by equation 0.75 x d (regular price) = final price. This means that to find the final price Nick will pay for any product it is required to multiply the regular price by 0.75.

This also means, Nick will pay 75% of the real price, and therefore the store is offering a 35% discount (100 - 75 = 35). This principle can be applied to find the price of the sweater.

Based on the previous information, let's calculate how much is the sweater:

$40 x 0.75 = $36

Based on this, Nick will pay $36 for the sweater.

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Answer:

60

Step-by-step explanation:

there are three sides to a triangle so 20x3 is 60 which is the perimeter

2 to the power of 4 is 16.

2^4 = (2 x 2 x 2 x 2) = 16

2 to the power of 4 is 16.

The answer to 2 to the power of 4 is 16. This means that 2 is multiplied by itself 4 times. To calculate this, it is easiest to start with the base number, 2. Then, multiply 2 by itself 3 more times. The result is 2 multiplied by 2 multiplied by 2 multiplied by 2, or 2 x 2 x 2 x 2, which equals 16. Therefore, 2 to the power of 4 is equal to 16.

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Answer:

-8

Step-by-step explanation:

(-2)^3 X (-2)^7 / 3X 4^6

= (-8) X (-128) / (3 X 4096)

= 1024 X -128 / 12288

= -128/12

= -8/1

So the final answer is -8

Answer:

1.398101×10^6

Step-by-step explanation:

(-2)^3×(-2)^7/3 ×4^6

=4194304/3

=1.398101×10^6

Since X, Y, and Z are independent random variables, the probability of one event occurring has no bearing on the likelihood of the other events. In this instance, the probabilities of X, Y, and Z are 30%, 40%, and 20%, respectively.

We must take into account the possibility that both events could occur simultaneously when determining the likelihood that either X or Y will occur. The occurrences where both X and Y occur would be doubly counted if we just added the probabilities of X and Y. To circumvent this, we employ the following formula for the chance of two events occurring together:

P(X or Y) = P(X) + P(Y) - P (X and Y)

This formula takes into account the fact that we must deduct the probability of X and Y's intersection (i.e., the likelihood that they both occur) from the total of each variable's individual probabilities.

Given that X and Y are independent events, P(X and Y) = P(X) * P(Y) = 0.3 * 0.4 = 0.12 is known.

P(X or Y) is therefore equal to P(X) + P(Y) - P(X and Y) = 0.3 + 0.4 - 0.12 = 0.68 = 68% 

 So, according to option most approximately option is A.

Therefore, 70% would be the most accurate response.

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Answer:

  neither

Step-by-step explanation:

You want to know if the graphed function is even or odd. It appears to be a cubic with a y-intercept of about 40.

Even functions are symmetrical about the y-axis. A function is even if ...

  f(x) = f(-x)

Even polynomial functions have terms that are all even powers of the variable.

Odd functions are symmetrical about the origin. A function is odd if ...

  f(x) = -f(-x)

Odd polynomial functions have terms that are all odd powers of the variable.

The graphed polynomial function has a non-zero added constant (the y-intercept value), so has both even and odd terms. It is neither even nor odd.

The graph is neither symmetrical about the y-axis, nor symmetrical about the origin.

Answer: Actually kinda ez not gonna lie. y = 11.547, x = 23.094

Step-by-step explanation: we know that y * square root of 3 = 20. 20/ root 3 is 11.547. Hypotenuse is 2 times y. This gives us x = 23.09

On solving the provided question, we can say that the linear equation, will be  10.50x + 12.50y = 4 => x = 23.1 => y = 3.21

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a large pizza costs =  $10.50 with no toppings other than cheese

Jason wants 4 toppings on his pizza for a cost of =  $12.10

the linear equation, will be

10.50x + 12.50y = 4

x = 23.1

y == 3.21

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The sequence will be; 8/49, 14/49, 20/49, 26/49

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We are given that the sequence as;

8/49, 2/7, 20/49, 26/49

so, we can see the pattern as the denominator is the multiple of 7.

So multiply the second term by 7.

2/7 = 14/49

therefore, the sequence will be;

8/49, 14/49, 20/49, 26/49

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Answer:

( 3a + b ) ( 2a − b )

Step-by-step explanation:

For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a • c = 6 • − 1 = − 6 and whose sum is b = − 1.

1) Reorder terms. = 6a^2 − b^2 − ab

2) Reorder −b^2 and − ab. = 6a^2 − ab − b^2

3) Factor −1 out of −ab. = 6a^2 − ( ab ) − b^2

4) Rewrite −1 as 2 plus −3. = 6a^2 + ( 2 − 3 ) ( ab ) − b^2

5) Apply the distributive property. = 6a^2 + 2 ( ab ) − 3 ( ab ) − b^2

6) Remove unnecessary parentheses. = 6a^2 + 2ab − 3 ( ab ) − b^2

7) Remove unnecessary parentheses. = 6a^2 + 2ab − 3ab − b^2

Factor out the greatest common factor from each group.
1) Group the first two terms and the last two terms.
= ( 6a^2 + 2ab ) − 3ab − b^2

2) Factor out the greatest common factor (GCF) from each group.
= 2a ( 3a + b ) − b ( 3a + b )

3) Factor the polynomial by factoring out the greatest common factor,
3a + b .

= ( 3a + b ) ( 2a − b )

Answer:

x = 1/2

y = 7/2

Step-by-step explanation:

Mate, you almost solved the question there by yourself.

You were at the last step.

-6x + 3 = 0

Add 6x on both sides,

-6x + 3 + 6x = 6x

3 = 6x

Divide 6 on both sides,

3/6 = 6/6 x

1/2 = x

So, y = 7x

y = 7/2

The expression becomes x-6 > 9 from the given condition The sum of a number and negative six greater than 9.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

To find the sum of a number and negative six , greater than 9 .

let the given number be x .

so,

the expression becomes ,

x - 6 > 9

LHS = x-6

as in the question its given the sum of number and negative of six

So whereas in RHS = 9

As it is given greater than 9 .

Hence, the expression becomes x-6 > 9 from the given condition.

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List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

What is congruent triangles ?

Congruent triangles are triangles that have the same size and shape. They can be matched up exactly, side-by-side, with no gaps or overlaps.

To list the six pairs of corresponding parts of congruent triangles using the triangle congruence statement, we can use the following steps ,

Begin by stating that the two triangles are congruent, using the triangle congruence statement such as "Triangles ABC and DEF are congruent by ASA, SAS, or SSS."

From the statement, we can determine the pairs of corresponding sides by noting which sides are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by ASA," we know that angle A in triangle ABC is congruent to angle D in triangle DEF, angle B in triangle ABC is congruent to angle E in triangle DEF and side AC in triangle ABC is congruent to side DE in triangle DEF

Next, we can determine the pairs of corresponding angles by noting which angles are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by SAS," we know that side AB in triangle ABC is congruent to side DE in triangle DEF, side BC in triangle ABC is congruent to side EF in triangle DEF, and angle A in triangle ABC is congruent to angle D in triangle DEF.

List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

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The required inequality describes the problem is  x ≤ 12.

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.

The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.

We have,

Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery.

let x represent how many more hours edna's phone can operate without running out of battery.

Then

x + 6 ≤ 18

x ≤ 12

Thus,required inequality is x ≤ 12.

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Answer: x = 3

Step-by-step explanation: Plug g(x) in to get 11 = 3x+2. Do algebra and you get x = 3

Answer:

Just put

a)

b)

c)

in the first column.

Next, substitute the values in the respective places.

For example, next to the a) and -3, put the value of y = x² + 1

In this case, 9 + 1 or 10

So, put 10 in the top left of the white spaces.

Hope you know what to do now.

Thanks

Answer:

Step-by-step explanation:

Using the formula of probability without replacement, the probability of selecting a heart first is 13 / 52 and a diamond second is 13 / 51

Probability without replacement refers to the likelihood of a specific event occurring when items are removed from a set or collection as they are selected. It differs from probability with replacement, where the items are replaced after each selection and the set remains unchanged.

To calculate probability without replacement, we use the formula:

P(Event) = Number of favorable outcomes / Number of possible outcomes

Where the number of possible outcomes is the total number of items in the set, and the number of favorable outcomes is the number of items that satisfy the conditions of the event.

In the first event;

P(heart) = 13 / 52

In the second event, the first card is not replaced and so, the number of possible outcomes is reduced by 1

p(diamond) = 13 / 51

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Answer:

Step-by-step explanation:

30-12/3=d

d=drinks he bought

$30-$12=$18

$18/$3=6

he got 6 drinks

Answer: -1 and 3

Step-by-step explanation:

The zeros of a function are where the graph of the function intersects the [tex]x[/tex]-axis.

Answer: -1 and 3

Step-by-step explanation:

        Finding the zeros of the function is the same as solving for the function, or what values of x make y equal 0. In this case, it is the x-intercepts, as shown by the graph. These values are  -1 and 3, see attached.

The inequalities to represent all of the constraints in Eric's problems using x for the number of adults and y for the number of children are as follows:

An inequality is a statement that compares two expressions using one of the following symbols: <, >, <=, >=, or ≠. The expressions being compared can be numbers, variables, or a combination of both.

The result of an inequality is either true or false. For example, the inequality 2x + 3y < 6 represents a set of ordered pairs (x,y) that satisfy the inequality. It describes all the points on a coordinate plane that fall under the solution set of the inequality.

From the inequalities above,

x + y <= 20 (maximum number of scuba divers) means that since the Lois Ann can only accommodate 20 scuba drivers, whether adults or children, their addition could be less than but not above 20

2x + y <= 30 (maximum number of tanks) means the capacity of Lois Ann is 30 tanks and the number of children is 10, and adult is 20, it implies that either all adults and all children or some adults participated twice (2x) plus children, it is their figure can be less than or equals to 30

20x + 10y <= 220 (maximum weight for scuba divers) implies that their entire weight whether adult or children cannot be more than 220

x, y >= 0 (non-negative number of adults and children) implies that no onee is undetermined of his placement as to whether such is adult or children.

Therefore, the correct answer is as given above

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Your adjusted gross income (AGI) consists of the total amount of income and earnings you made for the tax year minus certain adjustments to income. The dollar amount on line 10 is calculated by subtracting the standard deduction and personal exemptions from the taxable income.

Line 10 on the 1040EZ form is labeled "Taxable income" and is used to calculate the amount of taxes owed to the IRS. Line 11, labeled "Tax," is used to enter the amount of taxes already paid, either through withholding or estimated payments.

If $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS, that means that the amount of taxes already paid, $4184, is equal to the amount of taxes owed, which is calculated on line 10.

Therefore, the dollar amount on line 10 would also be $4184. This indicates that the taxpayer's taxable income and their taxes already paid are equal, resulting in no additional taxes owed or refund due.

It's worth noting that the dollar amounts on line 10 and line 11 are not directly related, the dollar amount on line 10 is calculated by subtracting the standard deduction and personal exemptions from the taxable income.

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Answer: x = 1

Step-by-step explanation: 4(1-x) = 6(x-1)

 -  4-4x = 6x-6

 -  6x-4x = 6-4

 -  2x = 2

 - x= 1

The rate of change of the hypotenuse is 9.5 inches per second.

The rate of change of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem. The theorem states that for a right triangle with sides of length a, b, and c (where c is the hypotenuse), a2 + b2 = c2.

In this case, we know that the two legs are 3 inches and 4 inches, and that the short leg is increasing by 7 in/sec and the long leg is growing at 9 in/sec.

Using the Pythagorean theorem, we can calculate the rate of change of the hypotenuse. We can set up the equation as follows: c2 = 32 + 42, where c is the hypotenuse. Solving for c, we get: c = √(32 + 42).

To calculate the rate of change of the hypotenuse, we need to take the derivative of the equation. Taking the derivative of the equation, we get: c' = (7/2) * (3/c) + (9/2) * (4/c).

Plugging in our values, we get: c' = (7/2) * (3/5) + (9/2) * (4/5). Simplifying, we get: c' = 9.5 in/sec.

Therefore, the rate of change of the hypotenuse is 9.5 inches per second.

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We add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

In the given question we have to find which polynomial should be added to [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex].

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

Let we add the polynomial P to get the polynomial [tex]3x^2 +4[/tex].

[tex]3x^3 - 2x^2 + 3[/tex] + P = [tex]3x^2 +4[/tex]

Subtract the equation [tex]3x^3 - 2x^2 + 3[/tex] on both side, we get

P = [tex]3x^2 +4[/tex] - ([tex]3x^3 - 2x^2 + 3[/tex])

P = [tex]3x^2 +4-3x^3 + 2x^2 - 3[/tex]

Now simplifying the expression

P = [tex]-3x^3 + 5x^2 +1[/tex]

So we add [tex]-3x^3 + 5x^2 +1[/tex] in the polynomial [tex]3x^3 - 2x^2 + 3[/tex] to get the polynomial [tex]3x^2 +4[/tex]. So the option 4 is correct.

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As per the given ratio, the diameter for the circle A is 8 cm.

The term diameter in math is defined as a straight line that goes from one side to the other side of a circle, passing through the center

Here we have given that Circle A is in the interior of circle B. The diameter of circle B is 16 cm.

And we need to find  the diameter of circle A in which the ratio of the shaded area to the area of circle A is 3:1.

While we looking into the given diagram, here we know that the area of the shaded region plus the area of circle A equals the Area of Circle B.

As we know that since the shaded area of the circle, 3:1,

And here we also have

=> 3x + x = 64π

When we simplify this one then we get,

=> 4x = 64π,

Then the value of x = 16π.

Here we have to directly we get

=> π x p² = 16π,

Then the value of

=> r² = 16

=> r = 4.

Here we must know that length can't be negative!

Therefore the diameter of circle A is

=> 4* 2 = 8 cm.

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Answer:

(1, 2)

Step-by-step explanation:

Looking at the graph, you can find the point of intersection. The point of intersection is over 1 on the x-axis, and next to 2 on the y-axis. So, the coordinate of the point of intersection is (1, 2).

Hope this helped!

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