If two cards are drawn without replacement, what is the probability of drawing at least one ace

Answer:

Option B is correct

Slope of the lines that passes through the given points is, [tex]\frac{-6}{5}[/tex]

Step-by-step explanation:

Given: The points (2 , 6) and (7 ,0).

Slope of a line identify the direction of a line. To find the slope, you divide the difference of the y-coordinates of two points on a line by the difference of the x- coordinates of those same two  points.

For any two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] the slope(m) of a line is given by;

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Now, substitute the point (2 ,6 ) and ( 7, 0) in the slope formula we have;

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}=\frac{0 - 6}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex]

therefore, the slope of the line that passes through the pair of points is;   [tex]\frac{-6}{5}[/tex]

Assuming that the cardboard forms a regular rectangle, therefore the area of the cardboard is simply taken to be the product of length and width. Therefore:

A = l w

A = (9 inches) * (4 inches)

A = 36 square inches = 36 inches^2

6/3 =2

15/3 =5

6/15 = 2/5

8/4 =2

20/4 =5

8/20 = 2/5

answer is B 2/5

Answer:

D

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

I can confirm, the first guy is right (I did the test)

The value in dollars of a stack of dimes that is 10 cm high is $10.

A dollar is further divided into some majorly used parts as:

A cent = 100th part of a dollar = $1/100 = $0.01

A nickle= 20th part of a dollar = $1/20 = $0.05

A dime = 10th part of a dollar = $1/10 = $0.10

A quarter = 4th part of a dollar = $1/4 = $0.25

If each dime is 1 mm then 10 dimes will be 1 cm high;

1 dime / 1 mm = x dimes / 10 mm Cross multiply

1 dime * 10 mm = x * 1 mm

10 dimes = x The mm

Since a dime is about 1 mm thick (10mm equals 1 cm), 10 cm high would be 100 dimes;

10 dimes = $1

$1 times 10 = $10

Hence, The value in dollars of a stack of dimes that is 10 cm high is $10.

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Power is the result of multiplying two numbers together. The solution of the x²=144 is ±12. The correct option is C.

Power is the result of multiplying two numbers together such that both numbers are equal to each other. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.

The solution of the given expression can be written as,

x² = 144

x² = 12×12  or -12×-12

x = √(12×12)  or √(-12×-12)

x = 12 or -12

x = ±12

Thus, the solution of the x²=144 is ±12. This is because the multiplication of two positive numbers is positive, also, the sum of the two negative numbers is positive.

Hence, the solution of the x²=144 is ±12

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The dice are illustrations of patterns

The fifth die that is different from the other four dice is die D

From the question, we have the following highlights

Hence, the fifth die that is different from the other four dice is die D

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To find the number of train cars and sections of wooden track in a full train set, we can set up a system of equations. The equations are 0.4x + 0.2y = 5.2 and 0.6x + 0.1y = 4.2.

To find the number of train cars and number of sections of wooden track in a full train set, we can set up a system of equations based on the given information.

Let's use x to represent the number of train cars and y to represent the number of sections of wooden track.

The system of equations that can be used to find the number of train cars and number of sections of wooden track in a full train set is:

0.4x + 0.2y = 5.2

0.6x + 0.1y = 4.2

Answer:

[tex](x+1)[/tex] and [tex](x-4)[/tex].

Step-by-step explanation:

We have been a trinomial [tex]x^2-3x-4[/tex]. We are asked to find the factors of our given trinomial.

We will use split the middle term to solve our given problem. We need to two number whose sum is [tex]-3[/tex] and whose product is [tex]-4[/tex]. We know such two numbers are [tex]-4\text{ and }1[/tex].

Split the middle term:

[tex]x^2-4x+x-4[/tex]

Make two groups:

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

Factor out GCF of each group:

[tex]x(x-4)+1(x-4)[/tex]

[tex](x-4)(x+1)[/tex]

Therefore, factors of our given trinomial are [tex](x+1)[/tex] and [tex](x-4)[/tex].

After 7 months her savings will be 7117.64.

Step-by-step explanation:

Given :

Rate is r = 5% = 0.05

Compounding interval, n = 12

Solution :

Now,

[tex]\rm \dfrac{r}{n} = \dfarc{0.05}{12}[/tex]

[tex]\rm \dfrac{r}{n} = 0.004167[/tex]

Now first deposit duration is 7 months. Therefore, its value is  [tex]\rm a_1 = 1000\times (1.004167)^7[/tex]

Now second deposit duration is 6 months. Therefore, its value is

[tex]\rm a_2 = 1000\times (1.004167)^6[/tex]

Now third deposit duration is 5 months. Therefore, its value is

[tex]\rm a_3 = 1000\times (1.004167)^5[/tex]

and so on.

The values are in geometric sequence where

[tex]\rm a = 1000\times (1.004167)[/tex]

[tex]\rm r = 1.004167[/tex]

We know that the sum of the geometric sequence is given by,

[tex]\rm S_n = \dfrac{a (r^n-1)}{(r-1)}[/tex]    ------ (1)

Now put the values of a and r in equation (1),

[tex]\rm S_7=\dfrac{1000\times(1.004167)((1.004167)^7-1)}{(1.004167-1)}[/tex]

[tex]\rm S_7 = 7117.64[/tex]

After 7 months her savings will be 7117.64.

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divide 400 by 24

400 / 24 = 16.666

 so they would need to buy 17 crates

The given problem consists of solving two inequalities. The first one, r4<−5, is invalid since the 4th power of any real number cannot be a negative number. For the second inequality, −2r−7 ≤ 3, the solution is r ≥ -5.

The subject of this question is Mathematics, specifically relating to solving inequalities. To answer your question, let's solve the two given inequalities independently. Starting with the first one, r4<−5, this inequality is invalid as the 4th power of any real number (r) cannot be less than -5. Moving on to the second inequality, −2r−7 ≤ 3, we first add 7 to both sides to isolate the term with the variable, giving us -2r ≤ 10. Dividing both sides by -2 (remember to flip the inequality sign when multiplying or dividing by a negative number) gives us r ≥ -5. Therefore, the solution to the given inequalities is r ≥ -5.

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Quadrilateral ABCD is inscribed in a circle. Let the measure of arc BAD be a°. Arcs BCD and BAD form a circle  and a circle measures 360°, then  measure of arc BCD is 360°-a°.

The inscribed angle theorem states that an angle  inscribed in a circle is half of the central angle  that subtends the same arc on the circle.

Because of the Inscribed angle theorem,

[tex]m\angle A=\dfrac{a^{\circ}}{2};[/tex]

[tex]m\angle C=\dfrac{360^{\circ}-a^{\circ}}{2}.[/tex]

The sum of the measures of angles A and C is

[tex]\dfrac{a^{\circ}}{2}+\dfrac{360^{\circ}-a^{\circ}}{2}=180^{\circ}.[/tex]

Therefore, angles A and C are supplementary, because their measures add up to 180°.

Angles B and D are supplementary, because the sum of the measures of the angles in a quadrilateral is 360°.

m∠A + m∠C + m∠B + m∠D = 360°,

and using substitution,

180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.

Answer: inscribed angle theorem

Answer:A

Step-by-step explanation:

Inscribed angle