jake has 16 toy cars. lydia has five fewer toy cars than jake. how many toy cars do they have in all?

If three bulbs are randomly selected, the probability that a) exactly 2 are 23 watts is 0.136, the probability that b) all are of the same type is 0.542 and c) there will be one bulb of each type is 0.244.

Here we have been given that out of 23 bulbs,

8 are 13 watt

9 are 18 watt

6 are 23 watt

now if three bulbs are randomly selected out of these, it can be done in

²³C₃ ways

a)

There are 6, 23 watts, and 17 bulbs that are not 23 watts.

Hence they can be chosen in

⁶C₂ X ¹⁷C₁ ways

Therefore the probability to get exactly 2 23 watt bulbs is

[⁶C₂ X ¹⁷C₁]/²³C₃

= [6 X 5 X 17 X 3 X 2]/[2 X 23 X 22 X 21]

= [3 X 5 X 17]/[23 X 11 X 7]

= 240/1771

= 0.136

b)

The probability that all three bulbs are of the same type will have three cases. Hence they can be selected in

⁸C₃ + ⁹C₃ + ⁶C₃ ways

Hence the probability will be

[⁸C₃ + ⁹C₃ + ⁶C₃]/²³C₃

= [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)](3 X 2)/[23 X 22 X 21]

=  [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)]/[23 X 11 X 7]

= [336 + 504 + 120]/1771

= 960/1771

= 0.542

c)

The probability to select one bulb of each type will be

[8 X 9 X 6]/²³C₃

= [8 X 9 X 6]/[23 X 11 X 7]

= 432/1771

= 0.244

d) Now if at least 6 bulbs need to be examined, hence

the probability will be 1 - probability that we need to check (1, 2, 3, 4, 5)

= 1 - (¹⁷C₀/23 + ¹⁷C₁/²³C₂ + ¹⁷C₂/²³C₃ + ¹⁷C₃/²³C₄ + ¹⁷C₄/²³C₅)

= 1 - (1/23 + 17/253 + 136/1771 + 136/1771 + 340/4807)

= 0.66

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Complete Question

A box in a supply room contains 23 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 6 are rated 23-watt. suppose that three of these bulbs are randomly selected. (round your answers to three decimal places.)

(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?

(b) What is the probability that all three of the bulbs have the same rating?

(c) What is the probability that one bulb of each type is selected?

(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

The parabola opens up, Axis of symmetry = 5, The quadratic have two solutions, x = 2 and x = 8 and And the vertex is a minimum.

Any geometric shape is divided into two equal halves by the symmetry. For a quadratic equation in standard form, y = ax2 + bx + c, the axis of symmetry formula is given as x = -b/2a. The equation is x = h if the parabola is in vertex form, which is y = a(x-h)2 + k.

Axis of symmetry = -b / 2a

x = 10 / 2(1)

x = 5

As axis of symmetry is x = 5,

the parabola opens up

Given the equation is y = x² - 10x + 16

factorizing the equation,

x² - 10x + 16

x² - 8x - 2x + 16

x(x - 8) -2(x - 8)

(x - 2)(x - 8)

x = 2 or x = 8

There are 2 solutions of parabola.

From the given equation,

x² - 10x + 16

Using completing squares method,

⇒ x² - 10x + 16 + 25 - 25

⇒ (x - 5)² - 9

The value of vertex (h, k) = (5,-9)

The vertex is minimum.

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Answer:

14

Step-by-step explanation:

let the number be x

3x=42

x=42/3

=14

The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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The sum of the first 6 terms of the geometric sequence 3, -6, 12, -24, ... is -3.

The first 6 terms of the geometric sequence 3, -6, 12, -24, ... can be calculated using the formula for the nth term of a geometric sequence:

[tex]a_n = a_1 * r^{(n-1)}[/tex]

where a_1 is the first term, a_n is the nth term, r is the common ratio, and n is the term number.

For the given sequence, a_1 = 3 and r = -2, so the first 6 terms can be calculated as follows:

[tex]a_2 = 3 * (-2)^{(2-1)} = -6\\a_3 = 3 * (-2)^{(3-1)} = 12\\a_4 = 3 * (-2)^{(4-1)} = -24\\a_5 = 3 * (-2)^{(5-1)} = 48\\a_6 = 3 * (-2)^{(6-1)} = -96\\[/tex]

The sum of the first 6 terms will be = 3 - 6 + 12 - 24 + 48 - 96 = -3

A geometric sequence is a number sequence in which the ratio of any two consecutive terms is always the same.

A geometric sequence has the following general form: a, ar, ar^2, ar^3,...,

where an is the first term of the sequence and r is the common ratio, which is a fixed number that represents the factor by which each term is multiplied to get the next term.

The formula for calculating the nth term of a geometric sequence is:

a_n = a * r(n-1) where n is the term number.

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The length of time it would have taken for both garden hoses to fill the pool would be 6.67 hours.

To solve this problem, we can use the formula:

1/rate = time

In the case of Joe's hose, the rate is 1/12 of the pool per hour. For his neighbor's hose, the rate is 1/15 of the pool per hour.

So, the combined rate is:

= (1/12) + (1/15)

= (5/60) + (4/60)

= 9/60 of the pool per hour

So, the time it will take to fill the pool using both hoses is:

= 1 / (9/60)

= 60/9 hours

= 6.7 hours

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The full question is:

Joe's garden hose fills the pool in 12 hours. His neighbor has thinner hose that fills the pool in 15 hours. How long will it take to fill the pool using both hoses?​

Answer:

8

Step-by-step explanation:

so first you need to add by the fraction of 10 the the BASS of eletro power of 10¬ then you add the μ3 that is how you get 8

To be certain that the angles created form a square inside a circle, it is important to first understand the properties of a square and a circle.

A square is a four-sided polygon with all sides of equal length and all angles of 90 degrees. This means that if we draw a square inside a circle, the four corners of the square should be tangent to the circle.

A circle is a shape with all points on the circumference equidistant from the center. This means that if we draw a square inside a circle, the distance from the center of the circle to the midpoint of each side of the square should be equal to the radius of the circle.

By verifying that the above two conditions are met, we can be certain that the angles created form a square inside the circle. Additionally, we can also check that all the four angle of the square is 90 degrees and the opposite sides are parallel.

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Answer:

330 approximately.

Step-by-step explanation:

The percentage lying between 2 standard deviations is 95%.

So we have 348 * 0.95 = 330 approximately.

The brain cancer with code is secondary malignant neoplasm of brain. So the option 3 is correct.

Some women experience persistent nerve pain (neuropathic pain) in the arm, armpit, or chest wall following breast cancer surgery. Due to the fact that it was originally identified in women who had mastectomies, this is known as post-mastectomy pain syndrome (PMPS), but it can also occur following other forms of breast-conserving surgery.

According to studies, 20% to 30% of women experience PMS symptoms following surgery. It most frequently occurs following procedures that remove tissue from the underarm or upper outer region of the breast.

It is crucial to discuss any pain you are experiencing with your doctor. You might not use your arm as you should because of PMPS, and eventually you might stop being able to use it normally.

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The complete question is:

Terry is post-mastectomy from breast cancer. Sadly, she has now found out that the cancer has metastasized to her parietal lobe of her brain. Report the brain cancer with code:

1. Benign neoplasm of brain, supratentorial

2. Malignant neoplasm of parietal lobe

3. Secondary malignant neoplasm of brain

4. Neoplasm of uncertain behavior of brain, supratentorial

The work done by the force of friction is μmgd.

The work done by the applied force is equal to the displacement of the block (d) multiplied by the component of the force parallel to the displacement. If the applied force is F and the angle between the force and the displacement is θ, then the component of the force parallel to the displacement is Fcos(θ).

Therefore, the work done by the applied force is given by dFcos(θ). The force of friction will also do work, which is equal to the displacement of the block multiplied by the force of friction. The force of friction is given by μN, where N is the normal force and is equal to the weight of the block (mg). Therefore, the work done by the force of friction is μmgd, where d is the displacement.

Correct Question :

A block of mass m is pulled along a horizontal surface by applying a force at an angle θ with the horizontal. If the block travels with a uniform velocity and has a displacement d and the coefficient of friction is μ, then the work done by the applied force is?

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Using a number line, the number 5/8 is greater than 2/4

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

Comparing 2/4 and 5/8 on a number line

Here is a number line that shows the comparison of 2/4 and 5/8:

 1/2         2/4    3/4     5/8   3/4     2/4         1/2

--|---------|---------|---------|---------|---------|--

As you can see, 2/4 is located halfway between 1/2 and 3/4, while 5/8 is located halfway between 3/4 and 3/4.

Therefore, 5/8 is larger than 2/4.

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The value of given function is (i) f(x²) = 2*x² and (ii) f(1) = 2*1 = 2.

A function is a link or expression that contains one or more variables. There is a collection of inputs and outputs.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input.

Applications of functions include population, distance traveled, and discovering profit. When using functions, one enters a number into the formula or locates the independent variable on a table or graph before computing the dependent variable that results.

(i) f(x²) = 2*x²

(ii) f(1) = 2*1 = 2

So, f(x²) = 2*x² and f(1) = 2

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The identities in verifying the trigonometric expression sinx cosx tanx=1-cos^2x include:

tanx = sinx/cosx

sin^2x+cos^2x = 1

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.

Anytime trigonometric functions are used in an expression or equation, trigonometric ifentities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity holds true. These trigonometric functions (such as sine, cosine, and tangent) of one or more angles are involved geometrically in these identities.

Based on the question, tanx = sinx/cosx and sin²x+cos^²x = 1 are applicable.

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What basic trigonometric identity would you use to verify that sinx cosx tanx=1-cos^2x

The size of the crowd is 7392 people.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

20 people fit comfortably in a 10 feet by 10 feet area.

So,

the ratio of the number of people per unit area = 20/(10 × 10) = 20/100 = 1/5

The area, A, occupied by the crowd = 7 feet × 1 mile × 1

1 mile = 5280 feet

A = 7 feet × 5280 feet × 1 = 36960 feet².

Now, number of people = 36960 x 1/5

= 7392 people.

Therefore, the required value is 7392 people.

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Fitness increases with energy intake rate was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying

Now, According to the question:

A parameter is used to describe the entire population being studied. For example, we want to know the average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

Fitness increases with energy intake rate varied by Lima, Valone and Caraco (1985) in their model of squirrel food carrying.

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The given question is incomplete, complete question is:

Mathematical models allow researchers to make different predictions by varying assumptions. Which of the following parameters was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying?

Answer:

Step-by-step explanation:

[tex]2x - (5-x) = 3x + 2(x-7)[/tex]

[tex]3x-5=3x+2(x-7)[/tex]

[tex]-5=2(x-7)[/tex]

[tex]-\cfrac{5}{2} =x-7[/tex]

[tex]-\cfrac{5}{2}+7=x[/tex]

[tex]-\cfrac{9}{2}=x[/tex]

[tex]x= \cfrac{9}{x}[/tex]

Therefore, the starting value of the house was £724,492.37 (rounded to two decimal places).

A fraction is a mathematical expression that represents a part of a whole. It is expressed as two numbers separated by a line or a slash, with the number on top called the numerator and the number on the bottom called the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. Fractions can be used to represent quantities such as lengths, distances, time, weight, and many other things in the real world. They are an important concept in mathematics and are used in a wide range of applications, from basic arithmetic to advanced calculus and beyond.

Here,

Let's denote the starting value of the house by x.

After the first year, the value increased by 9%, so the value became 1.09x.

After the second year, the new value decreased by 4%, so the value became 0.96(1.09x) = 1.0464x.

We know that this final value is £758,640, so we can set up an equation and solve for x:

1.0464x = 758640

x = 758640 / 1.0464

x ≈ 724492.37

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If the total price of the trip per student was $7.00, approximately the percentage of the trip that would go towards the price of the bus is 71.43%.

The percentage is the ratio of a variable or value to another.

Percentages are fractional values, computed as the quotient of a numerator over a denominator multiplied by 100.

The bus roundtrip charge per student = $5.00

The trip price per student = $7.00

Percentage of the trip going towards the price of the bus = 71.43% ($5/$7 x 100).

Thus, we expect that 71.43% of the trip amount will be consumed for the bus charter.

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To calculate the percent increase in airplane passenger capacity, we first need to find the difference between the current capacity (600 passengers) and the predicted future capacity (1400 passengers).

1400 - 600 = 800

Then divide this difference by the current capacity, and multiply by 100 to express the answer as a percentage.

(800/600) * 100 = 133.33

So the predicted percent increase in airplane passenger capacity is approximately 133%.

The nearest percent is 133%.

The volume of water in the ocean in litters,  5.6 x 10¹¹ L.    

In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms. The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.

The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.

In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms.

Volume is calculated as Area x Depth.

1.5 × 108/3700 = 5.6 x 10¹¹ L.    

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Answer:

Step-by-step explanation:

28

Graphs are used to represent information in bar graphs. Students can solve problems and comprehend relationships between quantities by using bar graphs to show such relationships.

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The expansion gives x² - 7x + 5x - 35

It is simplified to x = -5 and x = 7

An algebraic expression can be described as an expression that is comprised of terms, factors, constants, coefficients and variables.

They are also known to be made up of mathematical operations, such as;

From the information given, we have that;

(x+5)(x-7)

Now, expand the bracket

x² - 7x + 5x - 35

factorize in pairs

(x² - 7x) + (5x - 35)

factor the common terms

x(x - 7) + 5(x - 7)

then,

x = -5 and  x = 7

Thus, the expansion is x² - 7x + 5x - 35

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Answer:

90

Step-by-step explanation:

the bottom of the picture is cut off but it's 90°

becuase the picture shows you the 2 sides of the triangle r equal

the angles on the top are also equal

so that means the middle line has to be perpendicular to the base.

so Y is 90

The little cubes can be possible to remove in number of 18 cubes maximum.

What is cube ?

A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids.

The original surface area is (3x3) x 6 = 54 units.

A unit cube has 6 units of area, so we need 9 cubes.

Remove all the cubes except the original eight corners and the center cube.

The 3×3×3 cube has a surface area of 6×3×3 square units. Taking the 27 smaller units and connecting them to form a single entity, the maximum exposed surface area per cube is 6 square units. If nine of these are connected vertex to vertex in any shape then the objective is achieved. So a maximum of 18 of the small cubes can be removed.

Hence , The little cubes can be possible to remove in number of 18 cubes maximum.

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The integral[tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid, where f(x) is the side length of the square cross sections taken perpendicular to the x-axis in the region r.

The given integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid whose base is the region r. The integral is calculated by taking the cross sections of the solid perpendicular to the x-axis and consider them as squares. The side length of each square is denoted by f(x). The integral is calculated over the region r, which is the base of the solid. This integral is the sum of the areas of all the squares, which is equivalent to the volume of the solid. The integral is calculated by taking the lower limit of integration as[tex]$-\infty$[/tex] and the upper limit of integration as[tex]$\infty$[/tex]. Hence, the integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid with the base region r and square cross sections.

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During the first eighteen years of his rule, he spent most of his time defending his nation against attacks from Egypt, Italy, and the Mahdists.

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The genotype must be Rr and rr because the outcome is close to the 1:1 ratio of red to white flowering plants.

According to Mendel's law of dominance, one feature in a heterozygote will mask the existence of another trait for the same attribute. The dominant allele will be exclusively expressed, as opposed to both alleles contributing to a trait.

When parents with distinct, opposing qualities are crossed, only one form of the trait manifests itself in the offspring, according to Mendel's law of dominance. Only the dominant phenotypic characteristic will be present in the hybrid offspring. The first law of inheritance is the dominance principle.

This regulation states that the first generation of offspring from purebred parents shall exhibit solely dominant features.

There will be a 1:1 ratio between the dominant and recessive traits when a heterozygous dominant parent mates with a pure recessive parent.

The cross:

           r            r

R         Rr          Rr

r          rr           rr

The genotype must be Rr and rr since the outcome is close to the ratio of red to white flowering plants.

Therefore, the correct answer is option A. The result is close to the 1:1 ratio of red to white flowering plants, so the genotype must be Rr and rr.

The complete question is:

A cross between a plant with red flowers (R = dominant) and a plant with white flowers (r = recessive) yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plants? Explain

A. The results are close to a 1:1 ratio of plants with red flowers to plants with white flowers. Therefore, the genotypes of the Rr and ir

B. The results should yield plants with red flowers and plants with white flowers in a 3:1 ratio due, so the genotype of each parent is Rr. The number of offspring was not large enough to produce the expected results

C. The results differ from the predicted values. Therefore, the genotypes of the parents cannot be determined.

D. The results should show a ratio of 3 plants with white flowers to 1 plant with red flowers, so the genotypes of the parent plants are RR and rr.

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