Question 6
Sharron gets a total of £1050 each month.
She spends 3/10 of this on rent and 2/3 on food and bills.
How much money does Sharron have remaining?
Show your working out and write your answer in the box below.

Step-by-step explanation:

7!  =  7 P 7 = 5040 ways

7 choices for first

6 choices for 2nd

5 choices for 3rd

4 chouces for 4th

3

2

1

           7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!

The probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.

Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.

The probability that the spinner on the left will land on a 6 is calculated as,

P₁ = 2 / 12

The spinner on the right will land in a shaded area is,

P₂ = 8 / 12

The total probability will be,

P =  ( 2 / 12 ) x ( 8 / 12 )

P = 1 / 9

Therefore, the probability that the spinner on the left will land on a 6 and the spinner on the right will land on a shaded area will be 1/9. The correct option is A.

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Answer:

Yes it can be negative

Step-by-step explanation:

For example, in a vacuum, there is no atmospheric pressure and the pressure is zero. If we introduce a sealed container into the vacuum and pump out the air, the pressure inside the container will be negative compared to the pressure outside the container.

The solution of the system of equations is the point (-4, 0)

Here we have the system of equations:

y = -x - 4

4y - 2x = 8

To find the solutions graphically, what we need to do is graph both equations on the same coordinate axis, and then find the points where the graphs of the equations intercept. These points are the solutions of the system.

On the image at the end, you can see the graph of the system of equations, there we can see that the lines intercept at the point (-4, 0), so that is the solution.

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Answer:

0.0909

Step-by-step explanation:

4 blue + 5 red + 3 black = 12 chips in total.

p=probability

1st draw:

p (blue) = 4/12

there are now 11 chips in the bag, 4-1 =3 are blue.

2nd draw?

p (blue) = 3/11

probability of pulling one blue chip followed by another blue chip is:

(4/12) X (3/11) = (4X3)/12X11)

= (12)/(132)

= 1/11

0.0909

Answer:

I think it may be 160?

Step-by-step explanation:

400/5 is 80 there's 2 yellow so 2x80= 160 times

The fraction of the wall that is concrete is 12/19

A fraction is a mathematical representation of a part of a whole or a division of one quantity by another. It consists of two parts: a numerator and a denominator, separated by a horizontal line called a fraction bar or a division slash.

The numerator represents the number of parts or the quantity being considered, while the denominator represents the total number of equal parts or the divisor. The numerator and denominator are both whole numbers or integers.

In this problem, to determine the fraction that is concrete, we have to know the total length of the wall.

length of wall = 24 + 5 + 9 = 38 inches

The fraction of the wall that is concrete = 24 / 38 = 12/19

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Answer: $89 for one day and 70 miles

Step-by-step explanation:

An equation relating to P to N include the following: P(N) = 16.75N - 650.

In Mathematics, profit is a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling x number of books can be calculated by using the following function:

Profit made = Revenue earned – Cost of production (cost price)

P(N) = R(N) - C(N)

P(N) = 33.70N - (650 + 16.95N)

P(N) = 33.70N - 650 - 16.95N

P(N) = 16.75N - 650

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The error in solving the system of equations is given as follows:

Application of the negative signal, the distributive property must be applied instead of simply changing the signal of the first term.

The correct solution is:

(-10, -38).

The system of equations for this problem is defined as follows:

Replacing the second equation into the first, we have that:

2x - (4x + 2) = 18.

The negative sign changes the sign of all the terms inside the parenthesis, hence the value of x is obtained as follows:

2x - 4x - 2 = 18

-2x = 20

2x = -20

x = -10.

Then the value of y is given as follows:

y = 4(-10) + 2

y = -38.

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the measure of the angle that is supplementary to angle RST is 90 degrees

To determine the value of the angle, we need to know the following;

From the information given, we have that;

Angle RST is its own complement

Then, angle RST =90 degrees

The supplementary angle should be y

Then,

RST + y= 180

substitute the values

y = 180 - 90

subtract the values

y= 90 degrees

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The mass of the 405 cm³ milk is 417.15 grams.

Density is simply  the mass of a substance per unit volume.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Density of the milk p =  1.03g/cm³

Volume of the milk v = 405 cm³

Mass m = ?

Plug the values into the above formula and solve for mass m.

p = m / v

m = pv

m = 1.03g/cm³ × 405 cm³

m = 417.15 g

Therefore, the value of the mass is 417.15 grams.

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An expression that can be used to find the volume of the figure include the following: B. (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm).

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of figure = (2 cm × 8 cm × 7 cm) + (1 cm × 6 cm × 8 cm)

Volume of figure = 112 cm³ + 48 cm³

Volume of figure = 160 cm³

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Answer:

18 square units

Step-by-step explanation:

The parallelogram has been plotted in the attached figure

The area of a parallelogram is b x h

where b is one side and h is the vertical distance between the two bases

In the figure, we see that base = AB is parallel to the y-axis

This means the y-coordinates of A and B are the same and the distance is obtained by taking the absolute difference between the x-coordinates of A and B

b = |x1 - 2| = |6 - 0| = 6

The height h is a perpendicular line from point D(1, 3) to the base which touches the base at point E

Since this line is horizontal to the x-axis in the figure, the y coordinates of the endpoints of the line are the same i.e y1 =3 and y2 = 3

Therefore h = absolute difference between the x coordinates
= |1-4| = 3

Given b = 6, h = 3

area = 6x 3 = 18 square units

The number of unique preference orders that are represented in the table would be B. Five.

An individualized preference order is one way to assign a hierarchal ranking to an assortment of options. This ordering is recognized as "unique" because each item is assigned its own rank, with no two elements sharing the same level of priority.

From what is shown on the table, we have Voters 2, 4, 5 and 7 having a unique order. From these four voters, we therefore have four unique preference orders.

However, there is another unique preference order which is the shared preference order of Voters 1. 3 and 6 because this is unique preference order shared by three people.

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The value of total area of the shape is,

⇒ 82 cm²

We have to given that;

Figure of shape is shown.

Since, Figure is made by three rectangles.

And, Area of rectangle is,

A = length x width

Hence, The area of upper rectangle is,

A = 3 x 8

A = 24 cm²

Area of middle rectangle is,

A = (11 - (3 + 5)) x (8 - 2)

A = 3 × 6

A = 18 cm²

Area of lower rectangle is,

A = 5 x 8

A = 40 cm²

Thus, The value of total area of the shape is,

⇒ 24 + 18 + 40 cm²

⇒ 82 cm²

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Answer:

62.25

Step-by-step explanation:

this quadrilateral is a trapizoid

A = (a+b)/2 * h

a = x

b = 2.4+4.2+x

h = 7.5

we know x is 5 so we just plug it in

after doing that we get 62.25

The average weight of a sample of objects is 94.83 pounds and the spread of the weights around the mean is measured by the sample standard deviation, which is 31.16 pounds.

The given data shows the weights (in pounds) of adult wild mountain lions captured and released for the first time in the San Andres Mountains.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean weight x and sample standard deviation s.

[tex]x = (70 + 107 + 130 + 128 + 60 + 64) / 6 = 94.83 \pounds\\\\s = \sqrt{\frac{(70 - 94.83)^2 + (107 - 94.83)^2 + ... + (64 - 94.83)^2} {5}}[/tex]

= 31.16 pounds

Therefore, the sample mean weight x is 94.83 pounds and the sample standard deviation s is 31.16 pounds.

(b) To find a 75% confidence interval for the population average weight u of all adult mountain lions in the specified region, we can use the formula:

CI = x ± t*(s/√n)

where CI is the confidence interval, x is the sample mean weight, t is the t-score for the desired confidence level (75% in this case), s is the sample standard deviation, and n is the sample size (6 in this case).

From the t-table, the t-score for a 75% confidence level with 5 degrees of freedom is 2.015.

Plugging in the values, we get:

CI = 94.83 ± 2.015*(31.16/√6) = (63.6 pounds, 126.1 pounds)

Therefore, we can be 75% confident that the true population average weight of all adult mountain lions in the specified region is between 63.6 pounds and 126.1 pounds.

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The correct answer is option C: [tex]\(k + 4 = 16\).[/tex] This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

[tex]\[Tina = Kai + 4\][/tex]

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

[tex]\[16 = k + 4\][/tex]

This equation represents the fact that Tina has volunteered [tex]16[/tex] times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

[tex]\[k + 4 = 16\][/tex]

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: [tex]\(k + 4 = 16\).[/tex]

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The given function is tan (0+24°) and its cofunction can be expressed as ;tan (0+24°)=  tan (66⁰-0)

Therefore tan (0+24°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.

The complementary angle of 24° is 66° because 24° + 66° = 90°.

Using the formula for the sum of two angles, we can then substitute these values to get:

tan (0+24°)=  tan (66⁰-0)

Therefore, expression of tan (0+24°)in terms of its cofunctions is tan (0+24°) =  tan (66⁰-0)

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The surface area of the rectangular prism is 1476 square units

From the question, we have the following parameters that can be used in our computation:

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

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The corresponding angles and sides that show that the triangles are similar are: <A ≅ <R; <K ≅ <T; <M ≅ <L

RL/AM = RT/AK = TL/KM = 1.5.

Similar triangles are triangles that look alike but might be bigger or smaller than each other. This means that their matching or corresponding angles are the same and their matching sides have the same proportional length.

Therefore, from the image, we have corresponding pairs of angles that are congruent as follows:

Angles A and R

Angles K and T

Angles M and L

The corresponding sides that are proportional are:

AM and RL, which is RL/AM = 6/4 = 1.5

AK and RT, which is RT/AK = 7.5/5 = 1.5

KM and TL, which is TL/KM = 9/6 = 1.5

Therefore, the triangles are similar.

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Answer:

4 outcomes

Step-by-step explanation:

Answer:

(2x + 1) (x - 4)

Step-by-step explanation:

2x² - 7x - 4.

need two number that add up to -7, but that multiply together to get -4.

(2x + 1) (x - 4) = 2x² - 4(2x) + x - 4 = 2x²  - 8x + x - 4 = 2x²  - 7x - 4

Answer:

[tex]20x+240y/y[/tex]

Step-by-step explanation:

1. Subtract the numbers

2. Evaluate the exponents

3. Subtract the numbers, again

4. Have a great day and thx for your inquiry :)

The measure of angle RST is 90°.

option D.

The measure of angle RST is calculated by applying the principle of a right angle triangle as shown below;

A right-angled triangle, also known as a right triangle, is a triangle in which one of the angles measures exactly 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are known as the legs.

From the given diagram, the measure of angle RST is calculated as follows;

∠S = 90 (since this angle has a symbol of right angle)

So the other two angles, R and T are complementary.

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The total angle measurement of a triangle sum above is 180°. So yes,  it is possible to only make a right angle triangle but  impossible to draw a triangle

To check if a triangle can be drawn with 25°, 65°, and 90° angles, we use the Triangle Angle Sum Theorem stating that all triangle angles add up to 180 degrees.

If you add all the angles together (25 + 65 + 90 = 180°),  We can draw a triangle based on this sum, but we only consider the angles' nature. The triangle has angles of 25°, 65°, and 90°, making it a right triangle. It only applies to right triangle and not others triangle .

Note that based on the given angle measures of 25°, 65°, and 90°, it is impossible to draw a triangle as it does not follow the triangle inequality property.

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