A pair of dice are rolled. What is the probability of getting a sum greater then 7?

The expression 3(8 + 7) is equivalent to 45. The calculation follows the distributive property rule in mathematics, whereby we first simplify the expression inside the parentheses before multiplication.

The mathematical expression of 3(8 + 7) is based on the principle of distribution in mathematics. This principle can be interpreted as 'spread' or 'distribute' and applies when you multiply a number by addends within parentheses.

For the given expression 3(8 + 7), do the operation inside the parentheses first. So 8 + 7 equals 15. Now the expression becomes 3(15).

To find the solution, just multiply 3 by 15, which equals 45. So, 3(8 + 7) is equivalent to 45.

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Answer:

189 is the answer

Step-by-step explanation:

total bill would be X=6.00 +0.08m

where m = minutes

X = total bill

so 11.52 = 6.00+0.08m

subtract 6 from each side

5.52 = 0.08m

 now divide both sides by 0.08

5.52/0.08 = 69

 he was billed for 69 minutes.

Answer:

advance booking is cheaper by 400 bahts or $10.

Step-by-step explanation:

Car rental cost in advanced booking = $35 per day

and

when the rented locally it is charged = 1800 bahts per day

it is given that,

$1 is equal to 40 bahts.

now,

Car rental cost in advanced booking =  35  × 40

                                                              = 1400 bahts

hence, when booking is done advance

  the cost is cheaper  by  1800 - 1400 = 400 bahts

hence, advance booking is cheaper by 400 bahts or $10.

Answer: b. [tex]x\geq 0[/tex] , where x is the positive real numbers.

Step-by-step explanation:

We Know that, The Set of all Possible values of independent variable is called Domain of the function.

Since, Exponential graph starting at point (0, 30000),

Thus, the initial value of value of independent variable is 0.

Also,  The given exponential function is approaching the x axis as it moves left to right.

Therefore, The Domain must contain the all positive real numbers.

Thus, the Domain of the given function is [tex]x\geq 0[/tex] , where x is the positive real numbers.

Therefore, Option b is correct.

The question asks for the required contact area between a suction cup and a ceiling to support an 80.0 kg person. Using principles of physics pressure calculations, a suction cup with a minimum contact area of 7.74 cm² would be needed.

The subject of your question is physics given it requires an understanding of pressure, force, and area relationships. To keep the suction cup adhered, the pressure difference between the lower (inside) of the suction cup and the outside (room pressure) must be large enough to support the weight of the person. This principle makes use of a simple physics equation: Pressure = Force/Area.

To support an 80.0-kg person, the force exerted due to weight would be mass multiplied by gravity or 80.0 kg * 9.8 m/s² = 784 N. The atmospheric pressure is about 101,325 Pascal (Pa) or N/m². Rearranging the equation for Pressure will give us the needed area: Area = Force/Pressure. So, the necessary contact area would be 784 N / 101325 Pa ≈ 0.00774 m² or 7.74 cm².

This means, that in ideal conditions and neglecting factors such as surface roughness, a suction cup with a contact area of at least 7.74 cm² would be needed to support an 80.0-kg person.

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Answer:

The correct option is A.

Step-by-step explanation:

The general form of an ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.

From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is

[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]

The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.

[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]

[tex]0\leq 1[/tex]

This statement is true. The required inequality is

[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]

Therefore, the correct option is A.

The system of inequalities to determine the number of hamburger and hotdog buns Mr. Wu should purchase is x \\geq 2y for the quantity requirement, and 0.45x + 0.40y \\leq 60 for the budget constraint.

To determine how many hamburger buns (x) and hotdog buns (y) Mr. Wu can purchase for the concession stand, we need to set up a system of inequalities based on the given conditions. Since he needs at least twice as many hamburger buns as hotdog buns, we can express this requirement as an inequality: x \\geq 2y. Additionally, considering the cost of hamburger buns is $0.45 each and hotdog buns are $0.40 each, the total spending should not exceed $60. This gives us a budget constraint inequality: 0.45x + 0.40y \\leq 60. Therefore, the system of inequalities that can be used to determine the number of each kind of bun Mr. Wu should purchase is:

Answer:

65

Step-by-step explanation:

Final answer:

The smallest possible dimension for the null space of a 13 by 91 matrix is 78. This is determined using the Rank-Nullity Theorem, taking into account that the rank of a matrix cannot exceed the number of its rows.

Explanation:

The question pertains to the dimension of the null space (also known as the nullity) of a matrix 'a.' The dimensions of matrix 'a' are 13 by 91, which means it has 13 rows and 91 columns. The null space of a matrix 'a' is the set of all vectors that, when multiplied by 'a,' give the zero vector. The dimension of the null space is referred to as the nullity of 'a.'

To find the smallest possible dimension of the null space, we consider the Rank-Nullity Theorem, which states that for any matrix 'A' of size m by n, the rank of 'A' plus the nullity of 'A' is equal to n, the number of columns in 'A.' The maximum rank a matrix can have is limited by the smaller of the number of rows or columns, so for matrix 'a' with dimensions 13 by 91, the maximum rank is 13 since there are only 13 rows.

Using the Rank-Nullity Theorem, we can say:

Therefore, the smallest possible dimension for the null space of matrix 'a' is 78.

Answer:

Step-by-step explanation:

The act of reducing the selling price of products in order to attract costumers is called Price Reduction. This comprehends a marketing strategy.

To solve this problem, let us assume linear motion so that we can use the equation:

t = d / v

where t is time, d is distance and v is velocity

First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:

35 / Vu + 55 / Vd = 12                     ---> 1

30 / Vu + 44 / Vd = 10                     ---> 2

We rewrite equation 1 in terms of Vu:

(35 / Vu + 55 / Vd = 12) Vu

35 + 55 Vu / Vd = 12 Vu

12 Vu – 55 Vu / Vd = 35

Vu (12 – 55 / Vd) = 35

Vu = 35 / (12 – 55 / Vd)                  ---> 3

Also rewriting equation 2 to in terms of Vu:

Vu = 30 / (10 – 44 / Vd)                  ---> 4

Equating 3 and 4:

35 / (12 – 55 / Vd) = 30 / (10 – 44 / Vd)   

35 (10 – 44 / Vd) = 30 (12 – 55 / Vd)

Multiply both sides by Vd:

350 Vd – 1540 = 360 Vd – 1650

10 Vd = 110

Vd = 11 km / h

Using equation 3 to solve for Vu:

Vu = 35 / (12 – 55 / 11)

Vu = 5 km / h

Answers:

Vu = 5 km / h = velocity upstream

Vd = 11 km / h = velocity downstream

Answer:

Step-by-step explanation:

By definition, a quadrilateral is a general term for a parallelogram and a rhombus. They are both 4-sided two-dimensional shapes with two sets of parallel sides. However, a rhombus is a special case. It has equal sides. Consequently, all its angles are equal. Therefore, the resultant drawing is alike to what's in the attached picture. But technically, all its sides are equal to 6 cm and all its angles are equal to 80°.

Answer : Option A

Explanation:

we can clearly see that from x+ y=5 we can substitute  y = 5-x in y = 9x^2

Option B is clearly incorrect  x can not be y -5

Option C  is incorrect because y can not be 5 +x

Option D is incorrect because  its y = 9x^2 not y^2 =9x^2 so y can not be 3x

if its y^2 = 9x^2 then  only  implies y =  3x

Answer:

Option 1st is correct

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = 9x^2[/tex]      .....[1]

[tex]x+y = 5[/tex]         .....[2]

We can write equation [2] as:

[tex]y = 5-x[/tex]

Now, substitute this y value in [1] we have;

[tex]5-x= 9x^2[/tex]

Therefore, the system which is equivalent to the given system equation is,

[tex]5-x= 9x^2[/tex]

[tex]y = 5-x[/tex]

The plane was traveling at 319 miles per hour heading east. This was determined by setting up equations for the distances covered in both directions, considering the speed difference, and solving for the eastward speed.

To find the speed at which the plane was traveling east, we need to set up two equations based on the given information.

Let's denote the speed of the plane heading east  [tex]v_e[/tex] and the speed of the plane heading south [tex]v_s[/tex]. According to the problem, [tex]v_s[/tex] = [tex]v_e[/tex] + 45 mph. We also know that the plane flew south for 4 hours and east for 6 hours, covering a total distance of 3,370 miles.

To represent the sum of distances covered in both directions, we use the equation:

4[tex]v_s[/tex] + 6[tex]v_e[/tex] = 3,370

Substituting [tex]v_s[/tex] with [tex]v_e[/tex] + 45 in the equation yields:

4([tex]v_e[/tex] + 45) + 6[tex]v_e[/tex] = 3,370

By simplifying and solving for [tex]v_e[/tex], we find the speed of the plane traveling east. Let's solve it step by step:

4[tex]v_e[/tex] + 180 + 6[tex]v_e[/tex] = 3,370

10[tex]v_e[/tex] + 180 = 3,370

10[tex]v_e[/tex] = 3,190

[tex]v_e[/tex] = 319 mph

Therefore, the plane was traveling at 319 miles per hour heading east.

The solutions to the equation 15 tan^3 x=5 tan x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x =2.527, x = 5.669.

The trigonometric equation provided in the question is 15 tan3 x=5 tan x. We can start solving this equation by dividing both sides by tan x, which gives 15 tan2 x = 5. Dividing again by 5, we get tan2 x = 1/3. The solutions to tan2 x = 1/3 are values of x in the interval [0, 2π) where the square of the tangent of x equals 1/3. However, these values cannot be easily computed, thus we use a calculator to approximate the results. We find the solutions to the equation by considering all angles whose tangent is either sqrt(1/3) or -sqrt(1/3). Therefore, the solutions for x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x = 2.527, x = 5.669.

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To solve this problem, we make use of the z statistic. We are to look for the bottom 8% who has the shortest lifespan, this is equivalent to a proportion of P = 0.08. Using the standard distribution tables for z, the value of z corresponding to this P value is:

z = -1.4

Now given the z and standard deviation s and the mean u, we can calculate for the number of years of the shortest lifespan:

x = z s + u

x = -1.4 (0.7) + 2.4

x = -0.98 + 2.4

x = 1.42 years

Therefore the life span is less than about 1.42 years