First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4
Determine the scale factor used.
2
3
one third
one half
The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
Find the surface area and volume of the composite solid.
According to the information, the surface area of the solid is 758m² and the volume is 594m³
How to find the surface area of the solid?To find the surface area of the solid we have to perform the following procedure:
12m * 11m = 132m²
132m² * 2 = 264m²
16m * 9m = 144m²
144m² - 18m² = 126m²
126m² * 2 = 252m²
16m * 11m = 176m²
176m² - 66m² = 110m²
3m * 11m = 33m²
33m² * 2 = 66m²
6m * 11m = 66m²
264m² + 66m² + 66m² + 110m² +252m² = 758m²
To find the volume we have to perform the following procedure:
8m * 11m * 9m = 792m³
792m³ - 198m³ = 594m³
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a red car travels 20km in one hour .
a blue car travels 130km in the sAME TIME
which car thas greater average speed???
Answer:
The answer is the Blue car
Step-by-step explanation:
let Red car be x
let blue car be y
x=120km---->1hr
y=130km----->1hr
Average speed =distance(km)/time(hr)=km/hr
let A be average speed
A(x)=120/1=120km/hr
A(y)=130/1=130km/hr
therefore,
the blue car has the greatest average speed
Which is more, 19 ounces or 1 pound?
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.
Use L’hospital if it applies
Lim x—> infinity
(lnx)^3/x^2
The calculated value of the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
Calculating the limits of the derivativesTo apply L'Hopital's rule, we need to take the derivative of the numerator and denominator separately with respect to x.
We can apply this rule repeatedly until we get a determinate form.
lim x → ∞ [(ln x)^3 / x^2]
Taking the derivative of the numerator:
= 3(ln x)^2 (1/x)
Taking the derivative of the denominator:
= 2x
Applying L'Hopital's rule again by taking the derivative of the numerator and denominator:
= lim x → ∞ [6(ln x) / x]
Taking the derivative of the numerator:
= 6/x
Taking the derivative of the denominator:
= 1
Applying L'Hopital's rule one last time:
= lim x → ∞ 6 / x^2
= 0
Therefore, the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
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Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
A recliner is discounted by $190. If the original price is $800, estimate the sale price by first rounding each number to the nearest hundreds
all u got to do is subtract
differentiate with respect to x the implicit function sin(y)+x^2y^3-cos(x)=2y
Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
1. The radius of the circle is 3 units
2. The standard form of the equation is (x-1)^2+y^2=3
3. The center of the circle lies on X-axis
4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9
The given equation is: x^2+y^2-2x-8=0
The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle
The given equation in standard form can be written as
(x^2-2x+1)+y^2-9=0
(x-1)^2+y^2=3^2
Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.
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help please!! state the key features for this graph
Axis of symmetry: x = 1[tex]\\[/tex]
Vertex: (0,1)
Y-intercept: (0,1)
Min / Max: 0 / infinity
Domain: -infinity ≥ x ≥ infinity
Range: 0 ≥ y ≥ infinity
Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.
The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).
Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.
Therefore, the probability of drawing a green block followed by a yellow block is:
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%
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A factory received a shipment of 24 lightbulbs, and the vendor who sold the items knows there are 4 lightbulbs in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the lightbulbs in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 4 lightbulbs is selected, find the probability that all in the sample are defective. If a sample of 4 lightbulbs is selected, find the probability that none in the sample are defective.
The probability that none of the 4 lightbulbs in the sample are defective is 805/1763 as a reduced fraction.
What is probability?
Let's first calculate the total number of ways to choose 4 lightbulbs from 24:
24 choose 4 = (24!)/(4! * 20!) = 10,626
Probability that all 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose all 4 from the 24 is:
4 choose 4 = 1
So, the probability that all 4 lightbulbs in the sample are defective is:
1/10,626 = 1/5313
Therefore, the probability that all 4 lightbulbs in the sample are defective is 1/5313 as a reduced fraction.
Probability that none of the 4 lightbulbs in the sample are defective:
There are 4 defective lightbulbs in the shipment, so the number of ways to choose 4 non-defective bulbs from the remaining 20 is:
20 choose 4 = (20!)/(4! * 16!) = 4,845
So, the probability that none of the 4 lightbulbs in the sample are defective is:
4,845/10,626 = 805/1763
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Find the value of x please.
choices are..
16
19
18
15
Answer:
We have supplementary angles.
123 + 3x = 180
3x = 57
x = 19
Answer:
x = 19
Step-by-step explanation:
Angle on a straight line add up to 180
123 + 3x = 180
3x = 180 - 123
3x = 57
3x/3 = 57/3
x = 19
What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Therefore , the solution of the given problem of angles comes out to be the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.
An angle's meaning is what?The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.
Here,
Regarding the illustrated diagram, the appropriate statements are:
=> m∠3 + m∠4 + m∠5 = 180°
This is accurate since every triangle's internal angles add up to 180°.
=> m∠5 + m∠6 = 180°
This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.
=> m∠2 + m∠3 = m∠6
This is accurate because, based on the information provided,
the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.
Therefore, the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.
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5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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if a square has length of its side is 8cm then find length of its diagonal
Answer:
8√2 cm
Step-by-step explanation:
Explain what the constant of proportionality means in the equation y = 5/2 x
Answer:
[tex]y = \frac{5}{2} x[/tex]
[tex] \frac{y}{x} = \frac{5}{2} [/tex]
The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 44 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
What is cost?Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.
The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
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A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
Can you please help me with this.
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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I believe I missed the lesson on how to solve for x and y from this photo. Any help would be appreciated!
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
Explain about the Pythagorean theorem:The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the
a² + b² = c².
For the larger triangle, applying Pythagorean theorem:
4² + (4√3)² = x²
x² = 16 + 16*3
x² = 16 + 48
x² = 64
x = 8
Then, x - 6 = 8 - 6 = 2
Now applying Pythagorean theorem for smaller triangle:
y² + (x - 6)² = 4²
y² = 4² - 2²
y² = 16 - 4
y² = 12
y² = √12
y = 2√3
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
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Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answer:
Step-by-step explanation: