Prove these facts about matrices. (a) The row space of a matrix is isomorphic to the column space of its transpose. (b) The row space of a matrix is isomorphic to its column space.

The probability of choosing a red hat is 7/15

The given parameters are:

Red  = 14

Blue = 16

The probability of red is calculated as:

P(Red) = Red/Total

This gives

P(Red) = 14/30

Simplify

P(Red) = 7/15

Hence, the probability of choosing a red hat is 7/15

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The number of children that were admitted = 196

The number of adults that were admitted = 160

Given that,

The admission fee at an amusement park for children =  $1.25

The admission fee at an amusement park for adults = $6.80

On a certain day, people entered the park = 356

The admission fees collected totaled = $1333

Let us assume,

The number of children that were admitted represented as = x

The number of adults that were admitted represented as = y

On a certain day, 356 people entered the park.

So,

We can write,

x + y = 356  

x = 356 - y                                    (Equation-1)

The admission fee at the amusement park is $1.25 for children and $6.80 for adults.

The admission fees collected on that day totaled $1333.

Then the,

1.25x + 6.8y = 1333                      (Equation-2)

Substituting x = 356 - y into equation 2, it becomes

1.25x + 6.8y = 1333

1.25(356 - y) + 6.8y = 1333

445 - 1.25y + 6.8y = 1333

-1.25y + 6.8y = 1333 - 445

5.55y = 888

y = 888 / 5.55

y = 160

Then we can substitute y value in equation - 1,

x = 356 - y      

x = 356 - 160

x = 196

Therefore,

The number of children that were admitted = 196

The number of adults that were admitted = 160

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Answer:

44

Step-by-step explanation:

25dided by 4 is 6.25

multiply 6.25 and 7 and you'll get 43.75

round that to the nearest whole and you get 44

1. The linear function that models his distance from Washington, D.C. as a function of time, in hours, is:

d(t) = 109.5 - 55t.

2. The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is of: 0.9 hours = 54 minutes.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In the context of this problem, these parameters are given as follows:

Hence the function is:

d(t) = 109.5 - 55t.

The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is t when d(t) = 60.2 hence:

60.2 = 109.5 - 55t.

55t = 109.5 - 60.2

t = (109.5 - 60.2)/55

t = 0.9 hours = 54 minutes.

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Answer:

6.25

Step-by-step explanation:

divide the volume value by 8

Answer: Heres the answer for you

Step-by-step explanation:

And also how you work the promblem out also.

Answer: 3w - 9/2

When combining like terms and simplifying the equation, the answer is 3w - 9/2

Hope this helps =)

Answer:

ok so.u grit da he on 40/ rock cause u got a andriodnh on gf

Answer:

b? Ac should be Perpendicular to BD Or it might be A, but I'm pretty sure that it's B

Step-by-step explanation:

To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

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Answer:

The scale factor is 4

Step-by-step explanation:

This question requires an attachment; I'll answer this question using the attached figure

From the attachment

Length OA = 3 units

Length OA' = 3 units + 9 units

Length OA' = 12 units

Scale Factor is calculated as follows;

\(Scale\ Factor = \frac{New\ Side}{Original\ Side}\)

Given that the original shape is ABC, the original side will be OA

Hence, Original Side = 3 units

New Side = OA' = 12 units

The formula becomes

\(Scale\ Factor = \frac{12\ units}{3\ units}\)

\(Scale\ Factor = 4\)

Hence, the scale factor is 4

Answer:

4

Step-by-step explanation:

Just clarifying

Answer:

1.54 and 1.7 I believe

Step-by-step explanation:

Answer:

The full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Step-by-step explanation:

To find how many pounds each tire is, divide the weight in grams by 453.592

Full steel tire:

800/453.592 = 1.76 pounds

Lighter wheel:

700/453.592 = 1.54 pounds

So, the full steel tire is 1.76 pounds and the lighter wheel is 1.54 pounds

Answer:

123

Step-by-step explanation:

First of all, you have to find the total amount of people surveyed, so you add 82+105+141, which would be 328. Then you have to find 37.5% of 328, which is 123 only childs that have no pets.

Answer:

An expression is said to a perfect square trinomial if it takes the form ax2 + bx + c and satisfies the condition b2 = 4ac. The perfect square formula takes the following forms: (ax)2 + 2abx + b2 = (ax + b)

Step-by-step explanation:

Factor x2+ 6x + 9

Solution

We can rewrite the expression x2 + 6x + 9 in the form a2 + 2ab + b2 as;

x2+ 6x + 9 ⟹ (x)2 + 2 (x) (3) + (3)2

Applying the formula of a2 + 2ab + b2 = (a + b)2 to the expression gives;

= (x + 3)2

= (x + 3) (x + 3)

"In chemistry, a chemical equation is a symbolic representation of a chemical reaction. It uses chemical formulas to depict the reactants and products involved in the reaction."

Chemical equations are essential tools in chemistry as they provide a concise way to represent the substances undergoing a reaction and the products formed. They consist of chemical formulas for the reactants on the left-hand side, separated by an arrow from the formulas for the products on the right-hand side. The arrow indicates the direction of the reaction.

Chemical equations also include phase labels to indicate the physical state of each substance involved. These phase labels are written in parentheses next to the chemical formulas. Common phase labels include (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solution.

For example, the chemical equation for the reaction between sodium chloride and silver nitrate to form silver chloride and sodium nitrate would be:

NaCl(aq) + AgNO3(aq) → AgCl(s) + NaNO3(aq)

In this equation, NaCl(aq) and AgNO3(aq) represent the dissolved sodium chloride and silver nitrate in an aqueous solution, respectively. AgCl(s) denotes the silver chloride precipitate formed as a solid, and NaNO3(aq) indicates the sodium nitrate that remains dissolved.

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Answer:

46.67

Step-by-step explanation:

Answer:

Iam 5 yea4s old did you no that

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the smallest integer be x.

Then the other numbers are:

Sum of the four is 48:

Forming the equation,

→ x + (x + 2) + (x + 4) + (x + 6) = 48

→ 4x + 12 = 48

Now the value of x will be,

→ 4x + 12 = 48

→ 4x = 48 - 12

→ x = 36/4

→ [ x = 9 ]

Then smaller number is,

→ x = 9

Hence, the number is 9.

The sum of the given expression from n = 3 to 7 is 241.

The given expression is to be evaluated from n = 3 to 7.  The given expression is,begin{align*}\sum_{n=3}^{7} (n^2 + 2n)\end{align*}Now, we can substitute the values of n and add them up to evaluate the expression. So, the sum of the expression is, \begin{align*}\sum_{n=3}^{7} (n^2 + 2n) &= (3^2 + 2 \cdot 3) + (4^2 + 2 \cdot 4) + (5^2 + 2 \cdot 5) \\&\qquad+ (6^2 + 2 \cdot 6) + (7^2 + 2 \cdot 7)\\&= 9 + 20 + 35 + 72 + 105\\&= \boxed{241}.\end{align*}.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

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Answer:

  f(-3) = -20

Step-by-step explanation:

We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...

  34, 10, -8, ?

The first differences of these numbers are ...

  10 -34 = -24

  -8 -10 = -18

And the second difference is ...

  -18 -(-24) = 6

For a quadratic function, second differences are constant. This means the next first-difference will be ...

  ? -(-8) = -18 +6

  ? = -12 -8 = -20

The value of the function at x=-3 is -20.

_____

The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)

Answer: radius is 2.5 and volume of ice cream is 58.9 cm cubed

Step-by-step explanation:

Answer:

The area of the whole rectangle is 28 cm^2

Step-by-step explanation:

since both triangles are congruent, they have the same area. 14 x 2 = 28

Answer:

\(90 \times 40 = 3600\)

Step-by-step explanation:

i multiplied 9×4 and got the answer of 36 next i added the zeros from the numbers (90) and (40) and got my final answer whit is 3,600

2x＝ 3 -5√x using log form, x = log(2x + 5√x) = log(3)

To convert the equation 2x = 3 - 5√x into logarithmic form, we need to isolate the radical expression on one side of the equation. We can do this by adding 5√x to both sides:

2x + 5√x = 3

Next, we'll take the square root of both sides to eliminate the radical:

√(2x + 5√x)^2 = √(3^2)

Expanding the left side and simplifying:

2x + 5√x = 3

Finally, we'll take the logarithm of both sides to get x in logarithmic form:

log(2x + 5√x) = log(3)

To solve for x, we'll need to use logarithmic properties and/or exponential functions to isolate x on one side of the equation. log(2x + 5√x) = log(3)

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Answer:

Below

Step-by-step explanation:

The maximum area of land that can be enclosed is a SQUARE

  using the river as one side of the square means there are 3 sides that total 800 ft     800 / 3 = 266 2/3 ft per side

  area would then be L x W =    266 2/3  * 266 2/3 = 71111  1/9 ft^2

Answer:

Yes they are similar through AA similarity or Angle-Angle similarity.

Step-by-step explanation:

Vertical angles make an x and are always congruent. Those are HMG and JMK. Then you have two angles marked congruent with the same angle measure of 39, which are GHM and JKM. If two angles of a triangle are congruent, then all three have to be, so you just have to prove two angles to be congruent to prove the triangles similar.

Hope this helps :)

Answer:

(3,1)

Step-by-step explanation:

When a point is reflected across the y axis, the sign of its x coordinate flips. Since point A is at (-3,-5), when it is reflected across the y axis its new position will be (3,-5). Now, point A is 3 units from the line y=-2, meaning that when it is reflected across it will be 3 units away from the other direction. (-2+(3))=1, meaning that the final coordinates of point A are (3,1). Hope this helps!

Answer:

idek

Step-by-step explanation:

jk jk its -10 :)

Answer:

36 ft^2

Step-by-step explanation:

Perimeter = 4 + 4 + 2 +2 = 12 feet

  12 feet x 3 feet high = 36 ft^2

if a function is differentiable at a point, then it is continuous at that point is True.

If a function is differentiable at a point, it implies that the function is continuous at that point. The reason for this is that differentiability requires the existence of the derivative, which is based on the concept of a limit. And for a function to have a derivative at a point, it must also be continuous at that point. So, differentiability implies continuity.

what is continuity?

Continuity is a fundamental concept in calculus and analysis that describes the smooth and unbroken behavior of a function. A function is said to be continuous at a point if it does not have any abrupt jumps, holes, or vertical asymptotes at that point.

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Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal.

What is the congruency of triangles?

To show how can the triangles be proven similar by the SSS similarity theorem:

The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant

Reason:

Known parameters are:

ΔWUV and ΔXZY are shown:

∠VUW ≅ ∠YXZ

∠UWV ≅ ∠XZY

∠UVW ≅ ∠ZYX

Length of side VW = 60

Length of side VU = 50

Length of side UW = 40

Length of side  ZY = 48

Length of side  YX = 40

Length of side  XZ = 32

The ratio of the sides are:

\(\frac{VW}{ZY} =\frac{60}{48} =\frac{5}{4} \\\frac{VU}{YX} =\frac{50}{40} =\frac{5}{4} \\\frac{UW}{XZ} =\frac{40}{32} =\frac{5}{4}\)

Therefore, given that  the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by the Side-Side-Side SSS congruency theorem,  and we have:

ΔWUV ~ ΔYXZ given that ΔYXZ is a scaled drawing of ΔWUV.

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The complete question is given here:

Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.

How can the triangles be proven similar by the SSS similarity theorem?